The paper is to establish a boundedness criterion for some commutators of linear operators when these linear operators don't satisfy the general Ap weight estimates but satisfy some radial weight estimates.
We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algo...We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.展开更多
The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) ...The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) is a real-valued polynomial on R n× R n , Ω is homogeneous of degree zero, R m j (A j;x,y) denotes the m j -th order Taylor series remainder of A j at x expanded about y , M=∑kj=1 m j . It is shown that if Ω belongs to the space L log +L(S n-1 ) and has vanishing moment up to order M , then‖T A 1,A 2,…,A k f‖ q C ∏kj=1∑|α|=mj‖D αA j‖ r j ‖f‖ p, provided that 1<p,q<∞ , 1<r j ∞ (j=1,2,...,k) and 1/q=1/p+∑kj=1 1/r j . The corresponding maximal operator is also considered.展开更多
In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4...In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4r∈ [3～(1/2))2, 1). Moreover, we determine the range of parameter p with any given δ4r∈ [(3～(1/2))/22, 1). In fact, for any given δ4r∈ [3～(1/2))2, 1), p ∈(0, 2(1- δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices.展开更多
基金National Natural Science Foundation of China(No.1 990 1 0 2 1 ) and Beijing Ed-ucation Commission FoundationNatural Science Foundation of Beijing (1 0 1 3 0 0 6)
文摘The paper is to establish a boundedness criterion for some commutators of linear operators when these linear operators don't satisfy the general Ap weight estimates but satisfy some radial weight estimates.
基金supported by NSFC(Nos.11271050,11371183)Li was partially supported by NSFC(No.11171026)+1 种基金the Fundamental Research Funds for the Central Universities(No.2014kJJCA10)Beijing Higher Education Young Elite Teacher Project
基金National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)
文摘We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.
文摘The authors consider the multilinear oscillatory singular integral operator defined by T A 1,A 2,…,A k f(x)=∫ R n e iP(x,y) ∏k j=1 R m j (A j;x,y)Ω(x-y)|x-y| n+M f(y)dy,where P(x,y) is a real-valued polynomial on R n× R n , Ω is homogeneous of degree zero, R m j (A j;x,y) denotes the m j -th order Taylor series remainder of A j at x expanded about y , M=∑kj=1 m j . It is shown that if Ω belongs to the space L log +L(S n-1 ) and has vanishing moment up to order M , then‖T A 1,A 2,…,A k f‖ q C ∏kj=1∑|α|=mj‖D αA j‖ r j ‖f‖ p, provided that 1<p,q<∞ , 1<r j ∞ (j=1,2,...,k) and 1/q=1/p+∑kj=1 1/r j . The corresponding maximal operator is also considered.
基金supported by National Natural Science Foundation of China(Grant Nos.11271050 and 11371183)Beijing Center for Mathematics and Information Interdisciplinary Sciences
文摘In this paper, a sufficient condition is obtained to ensure the stable recovery(ε≠ 0) or exact recovery(ε = 0) of all r-rank matrices X ∈ Rm×nfrom b = A(X) + z via nonconvex Schatten p-minimization for anyδ4r∈ [3～(1/2))2, 1). Moreover, we determine the range of parameter p with any given δ4r∈ [(3～(1/2))/22, 1). In fact, for any given δ4r∈ [3～(1/2))2, 1), p ∈(0, 2(1- δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices.
