This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ （G） named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups
Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b（x） ∈ CBMOq （Rn） on homogeneous Morrey-Herz spaces is established.
Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional ...Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b（x） in BMO（R^n）, respectively.展开更多
In this paper, by establishing the boundedness results of singular integral operators and linear commutators, we obtain the global regularity, in homogeneous Morrey-Herz spaces, of strong solutions to nondivergence el...In this paper, by establishing the boundedness results of singular integral operators and linear commutators, we obtain the global regularity, in homogeneous Morrey-Herz spaces, of strong solutions to nondivergence elliptic equations with VMO coefficients.展开更多
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
. In this paper,the characterization of boundedness of Hardy-Littlewood maximal operators in Orlicz-Morrey spaces LΦφ（X,μ） of homogeneous type is founded.
Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on ...Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.展开更多
Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via diffe...Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.展开更多
A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the r...The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.展开更多
An equivalent definition of fractional integral on spaces of homogeneous type is given. The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset ...This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.展开更多
In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P（G） and HKq^α,P（G）, where 1 〈 q 〈 ∞, Q（1 - 1/q） ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie ...In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P（G） and HKq^α,P（G）, where 1 〈 q 〈 ∞, Q（1 - 1/q） ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.展开更多
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit p...We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.展开更多
We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a func...Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.展开更多
Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associa...Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.展开更多
基金Supported by Mudanjiang Teachers College (KZ2008001)by Scientific Research Fund of Heilongjiang Provincial Education Department(No.11541378)
文摘This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ （G） named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups
基金Supported by NSF of China (10371087)NSF of Anhui Province(07021019)Education Committee of Anhui Province(KJ2007A009)
文摘Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
基金NSFC(10571014)NSFC(10571156)+1 种基金the Growth Foundation of JXNU(1983)the Doctor Foun-dation of JXNU
文摘The boundedness of the commutator μΩ,b generalized by Marcinkiewicz integral μΩ and a function b（x） ∈ CBMOq （Rn） on homogeneous Morrey-Herz spaces is established.
基金the National Natural Science Foundation of China(1057101410571158).
文摘Some boundedness results are established in the setting of homogeneous Morrey-Herz spaces for a class of higher order commutators T^mb,l and M^mb,l generated by fractional integral operators Tl and maximal fractional operators Ml with function b（x） in BMO（R^n）, respectively.
文摘In this paper, by establishing the boundedness results of singular integral operators and linear commutators, we obtain the global regularity, in homogeneous Morrey-Herz spaces, of strong solutions to nondivergence elliptic equations with VMO coefficients.
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
文摘. In this paper,the characterization of boundedness of Hardy-Littlewood maximal operators in Orlicz-Morrey spaces LΦφ（X,μ） of homogeneous type is founded.
基金Supported by Natural Science Foundation of Xinjiang University Supported by the NNSF of Chlna（10861010） Supported by Research Starting Foundation for Doctors of Xinjiang University（BS090102）
文摘Under certain weak local size conditions, the boundedness of linear commutators on Herz-Morrey spaces on spaces of homogeneous type are studied. In addition, the boundedness of Hardy-Littlewood maximum commutators on Herz-Morrey spaces on spaces of homogeneous type are obtained.
文摘Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense.
文摘A new maximal function is introduced in the dual spaces of test function spaces on spaces of homogeneous type. Using this maximal function, we get new characterization of atomic H^p spaces.
基金Project 19871071 supported by Natural Science Foundation of China
文摘The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.
文摘An equivalent definition of fractional integral on spaces of homogeneous type is given. The behavior of the fractional integral operator in Triebel-Lizorkin space is discussed.
文摘This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.
基金Supported by National Science Foundation of China, No. 10261007.
文摘In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P（G） and HKq^α,P（G）, where 1 〈 q 〈 ∞, Q（1 - 1/q） ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.
文摘We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.
基金Supported by the National Natural Science Foundation of China(Nos.10771049, 60773174)the Natural Science Foundation of Hebei Province (08M001)
文摘We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
基金Supported by the National Natural Science Foundation of China
文摘Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.
文摘Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.
