This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.
Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm ...In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.展开更多
Due to the limitation of Depth Of Field (DOF) of microscope, the regions which are not within the DOF will be blurring after imaging. Thus for micro-image fusion, the most important step is to identify the blurring re...Due to the limitation of Depth Of Field (DOF) of microscope, the regions which are not within the DOF will be blurring after imaging. Thus for micro-image fusion, the most important step is to identify the blurring regions within each micro-image, so as to remove their undesirable impacts on the fused image. In this paper, a fusion algorithm based on a novel region growing method is proposed for micro-image fusion. The local sharpness of micro-image is judged block by block, then blocks whose sharpness is lower than an adaptive threshold are used as seeds, and the sharpness of neighbors of each seed are evaluated again during the region growing until the blurring regions are identified completely. With the decreasing in block size, the obtained region segmentation becomes more and more accurate. Finally, the micro-images are fused with pixel-wise fusion rules. The experimental results show that the proposed algorithm benefits from the novel region segmentation and it is able to obtain fused micro-image with higher sharpness compared with some popular image fusion method.展开更多
By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbo...By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L es...Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.展开更多
Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space...Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space Lipa（R^n）with a∈（0,1）,the commutator [b,V1/2A^-1/2]is bounded from L^p（R^n）to L^q（R^n）,where p,q∈（1,2] and 1/p-1/q=a/n.展开更多
By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function,the weak type LlogL estimates for the commutators of the fraction...By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function,the weak type LlogL estimates for the commutators of the fractional integral operator and the related maximal operator are established.展开更多
In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf...Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.展开更多
In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the bound...In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.展开更多
A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color.The minimum number of colors required to color the edges of G such that every pair of vertices are conn...A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color.The minimum number of colors required to color the edges of G such that every pair of vertices are connec ted by at least k internally ver tex-disjoint rainbow paths is called the rainbow k-connectivity of the graph G,denoted by rck(G).For the random graph G(n,p),He and Liang got a sharp threshold function for the property rck(G(n,p))≤d.For the random equi-bipartite graph G(n,n,p),Fujita et.al.got a sharp threshold function for the property rck(G(n,n,p))≤3.They also posed the following problem:For d≥2,determine a sharp threshold function for the property rck(G)≤d,where G is another random graph model.This paper is to give a solution to their problem in the general random bipartite graph model G(m,n,p).展开更多
Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As ...Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.展开更多
This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO fu...This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.展开更多
We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation.
In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A_(∞).Moreover,weigh...In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A_(∞).Moreover,weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.展开更多
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
文摘This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
文摘In this article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
基金Supported by the Natural Science Foundation of Hebei Province (08M001)the National Natural Science Foundation of China (10771049)
文摘For maximal multilinear Calderon-Zygmund singular integral operators, the sharp maximal function estimate and some weighted norm inequalities are obtained.
基金Research supported by Council of Scientific and Industrial Research, India under award no.9/143(163)/91-EER-
文摘Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.
文摘In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the L<sup>p</sup> (1 p norm inequalities for the multilinear operators.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y1101240)Zhejiang Scientific and Technical Key Innovation Team (2010R50009)+1 种基金Natural Science Foundation of Ningbo (2011A610200, 2011A610197)Student Research and Innovation Training Program of Zhejiang Province (New-shoot Talents Project 2011R-405054) (A00162100400)
文摘Due to the limitation of Depth Of Field (DOF) of microscope, the regions which are not within the DOF will be blurring after imaging. Thus for micro-image fusion, the most important step is to identify the blurring regions within each micro-image, so as to remove their undesirable impacts on the fused image. In this paper, a fusion algorithm based on a novel region growing method is proposed for micro-image fusion. The local sharpness of micro-image is judged block by block, then blocks whose sharpness is lower than an adaptive threshold are used as seeds, and the sharpness of neighbors of each seed are evaluated again during the region growing until the blurring regions are identified completely. With the decreasing in block size, the obtained region segmentation becomes more and more accurate. Finally, the micro-images are fused with pixel-wise fusion rules. The experimental results show that the proposed algorithm benefits from the novel region segmentation and it is able to obtain fused micro-image with higher sharpness compared with some popular image fusion method.
文摘By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function,multilinear commutators of fractional integral operator with vector symbol b=(b 1,...,b m)defined byI b αf(x)=∫ R∏mj=1(b j(x)-b j(y))1｜x-y｜ n-αf(y)dyare considered.The following priori estimates are proved.For 1<p<∞,there exists a constant c such that‖I b αf‖ Lp(Rn)≤c‖b‖‖M L(logL) 1r,α(f)‖ Lp(Rn),So‖I b αf‖ Lq(Rn)≤c‖b‖‖f‖ Lp(Rn),where 1<p<nα,1q=1p-αn,0<α<n,and supt>01Φ1t｜｛y∈Rn:｜I b αf(y)｜>t｝｜ 1q≤ c supt>01Φ1t｜｛y∈Rn:M L(logL) 1r,α(‖b‖f)(y)>t｝｜ 1q,where ‖b‖=∏ m j=1‖b j‖ Osc expL r j,Φ(t)=t(1+log+t) 1r,1r=1r 1+...+1r m, M L(logL) 1r,α is an Orlicz type maximal operator.
基金The Science and Technology Research(Z2014057)of Higher Education in Hebei Provincethe Doctoral Foundation(L2015B05)of Hebei Normal Universitythe NSF(A2015403040)of Hebei Province
文摘Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.
基金supported by the National Natural Science Foundation of China (No.11671031 and No.11471018)the Fundamental Research Funds for the Central Universities (No.FRF-BR-17-004B)Program for New Century Excellent Talents in University,Beijing Municipal Science and Technology Project (No.Z17111000220000)
文摘Let A=-（ -ia）·（ -ia）＋V be a magnetic Schrodinger operator on L^2（R^n）,n〉2,where a：=（a1,…,an）∈Lloc^2（R^n,R^n） and 0≤V ∈Lloc^1（R^n）.In this paper, we show that for a function b in Lipschitz space Lipa（R^n）with a∈（0,1）,the commutator [b,V1/2A^-1/2]is bounded from L^p（R^n）to L^q（R^n）,where p,q∈（1,2] and 1/p-1/q=a/n.
基金This work was supported by 973 Project of China, the National Natural Science Foundation of China (Grant No. 19971010) and DPFIHEC (Grant No. 98002703).
文摘By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function,the weak type LlogL estimates for the commutators of the fractional integral operator and the related maximal operator are established.
基金supported by National Natural Science Foundation of China (Grant No.10701010) the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry+1 种基金supported by National Natural Science Foundation of China (Grant No.10571015) Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050027025)
文摘In this paper, weighted Lp estimates and sharp weighted endpoint estimates for the mul-tilinear commutators of the Littlewood-Paley operators are established.
基金Hei Long Jiang Postdoctoral Foundation (LBH-Q06002)
文摘Let μ be the n-dimensional Marcinkiewicz integral and μb the multilinear commutator of μ. In this paper, the following weighted inequalities are proved for ω ∈ A∞ and 0 〈 p 〈 ∞,｜｜μ（f）｜｜LP（ω）≤C｜Mf｜LP（ω） and ｜｜μb（f）｜｜LP（ω）≤C｜｜ML（log L）^1/r f｜｜LP（ω）.The weighted weak L（log L）^1/r -type estimate is also established when p=1 and ω∈A1.
基金Supported by the National Natural Science Foundation of China(Grant No.11671397)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)+1 种基金the State Scholarship Fund of Chinathe Yue Qi Young Scholar of China University of Mining and Technology(Beijing)
文摘In this paper, the authors study a class of multilinear singular integral operators with generalized kernels and their multilinear commutators with BMO functions. By establishing the sharp maximal estimates, the boundedness on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces is obtained, respectively. Moreover, the endpoint estimate of this class of mutilinear singular integral operators is also established. These results can improve the corresponding known results of classical multilinear Calder6n-Zygmund operators and multilinear Calderon-Zygmund operators with Dini type kernels.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11871034,11531011)by the Natural Science Foundation of Jiangsu Province(No.BK20150169).
文摘A path in an edge-colored graph G is called a rainbow path if no two edges of the path are colored the same color.The minimum number of colors required to color the edges of G such that every pair of vertices are connec ted by at least k internally ver tex-disjoint rainbow paths is called the rainbow k-connectivity of the graph G,denoted by rck(G).For the random graph G(n,p),He and Liang got a sharp threshold function for the property rck(G(n,p))≤d.For the random equi-bipartite graph G(n,n,p),Fujita et.al.got a sharp threshold function for the property rck(G(n,n,p))≤3.They also posed the following problem:For d≥2,determine a sharp threshold function for the property rck(G)≤d,where G is another random graph model.This paper is to give a solution to their problem in the general random bipartite graph model G(m,n,p).
基金This work was supported by the National Natural Science Foundation of China of China （Grant No. 11571289）.
文摘Let γ be the Gauss measure on Rn. We establish a Calderon- Zygmund type decomposition and a John-Nirenberg type inequality in terms of the local sharp maximal function and the median value of function over cubes. As an application, we obtain an equivalent characterization of known BMO space with Gauss measure.
基金supported by the National Natural Science Foundation of China(Nos.10961015,11261023)the Jiangxi Natural Science Foundation of China(No.20122BAB201011)the Fund of Jiangxi Provincial Department of Education(Nos.GJJ10397,GJJ12203)
文摘This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.
基金Supported by National Science Foundationof China (Grant Nos. 10571156 and 10871173)
文摘We prove endpoint estimates for maximal commutators for a class of singular integral operators related to the real analysis of the Monge Ampere equation.
文摘In this article,we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type.The weightωconsidered here belongs to the Muckenhoupt’s class A_(∞).Moreover,weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.
