In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essential...In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.展开更多
Let Ω be a function of homogeneous of degree zero and satisfy the cancellation condition on the unit sphere. Suppose that h is a radial function. Let Th,Ω,φ be the classical singular Radon transform, and let Th^ε,...Let Ω be a function of homogeneous of degree zero and satisfy the cancellation condition on the unit sphere. Suppose that h is a radial function. Let Th,Ω,φ be the classical singular Radon transform, and let Th^ε,Ω,φ be its truncated operator with rough kernels associated to polynomial mapping which is defined by Th^ε,Ω,φf(x)=|f|y|>εf(x-φ(y))h(|y|)Ω(y)|y|^-ndy|.In this paper, we show that for any a ∈(-∞,∞) and (p, q) satisfying certain index condition, the operator Th^ε,Ω,φ enjoys the following convergence properties lim ε→0||Th^ε,Ω,φf-Th,Ω,φf||Fα^p,q(R^d)= 0 and limε→0||Th^ε,Ω,φf-Th,Ω,φf||Bα^p,q(R^d)=0, provided that Ω∈L(log+ L)β(S^n-1) for some β∈(0,1], or Ω∈H^1(S^n-1), or Ω∈(U1<q<∞Bq^(0,0)(S^n-1)).展开更多
In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and contin...In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.展开更多
Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)...Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).展开更多
基金supported by the National Natural Science Foundation of China(Nos.11871101,12171399)NSFC-DFG(No.11761131002)+3 种基金the Natural Science Foundation of Fujian Province(No.2021J05188)the Scientific Research Project of The Education Department of Fujian Province(No.JAT200331)the President’s fund of Minnan Normal University(No.KJ2020020)the Institute of Meteorological Big Data-Digital Fujian,Fujian Key Laboratory of Data Science and Statistics and Fujian Key Laboratory of Granular Computing and Applications(Minnan Normal University)。
文摘In this paper,the authors show that the maximal operators of the multilinear Calderón-Zygmund singular integrals are bounded from a product of weighted Hardy spaces into a weighted Lebesgue spaces,which essentially extend and improve the previous known results obtained by Grafakos and Kalton(2001)and Li,Xue and Yabuta(2011).The corresponding estimates on variable Hardy spaces are also established.
文摘Let Ω be a function of homogeneous of degree zero and satisfy the cancellation condition on the unit sphere. Suppose that h is a radial function. Let Th,Ω,φ be the classical singular Radon transform, and let Th^ε,Ω,φ be its truncated operator with rough kernels associated to polynomial mapping which is defined by Th^ε,Ω,φf(x)=|f|y|>εf(x-φ(y))h(|y|)Ω(y)|y|^-ndy|.In this paper, we show that for any a ∈(-∞,∞) and (p, q) satisfying certain index condition, the operator Th^ε,Ω,φ enjoys the following convergence properties lim ε→0||Th^ε,Ω,φf-Th,Ω,φf||Fα^p,q(R^d)= 0 and limε→0||Th^ε,Ω,φf-Th,Ω,φf||Bα^p,q(R^d)=0, provided that Ω∈L(log+ L)β(S^n-1) for some β∈(0,1], or Ω∈H^1(S^n-1), or Ω∈(U1<q<∞Bq^(0,0)(S^n-1)).
基金supported by National Natural Science Foundation of China(Grant No.11701333)Support Program for Outstanding Young Scientific and Technological Top-Notch Talents of College of Mathematics and Systems Science(Grant No.Sxy2016K01)+3 种基金supported by National Natural Science Foundation of China(Grant Nos.11471041 and 11671039)National Natural Science Foundation of China-Deutsche Forschungsgemeinschaft(Grant No.11761131002)supported by Grant-in-Aid for Scientific Research(C)(Grant No.15K04942)Japan Society for the Promotion of Science。
文摘In this paper,we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in Fβ(S^n-1),a topic that relates to the Grafakos-Stefanov class.The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.
文摘Let I_(α,→b)be the multilinear commutators of the fractional integrals Iαwith the symbol→b=(b1,……,bk)We show that the constant of borderline weighted estimates for Iαis I/ξ,and for I_(α,→b)is with each b_(i)belongs to the Orlicz space Osc_(exp L^(si)).
