Estimates of Some Integral Operators with Bounded Variable Kernels on the Hardy and Weak Hardy Spaces over R^n

作     者：Hua WANG 

作者机构：College of Mathematics and EconometricsHu'nan University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2016年第32卷第4期

页      面：411-438页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Singular integral operators fractional integrals parametric Marcinkiewicz integrals variable kernels Hardy spaces H^p(R^n) weak Hardy spaces WH^p(R^n) Hardy-Lorentz spaces Hp,q(Rn) 

摘      要：In this paper,we first introduce Lσ1-（log L）σ2 conditions satisfied by the variable kernelsΩ（x,z） for 0≤σ1≤1 and σ2≥*** these new smoothness conditions,we will prove the boundedness properties of singular integral operators TΩ,fractional integrals TΩ,α and parametric Marcinkiewicz integrals μΩρ with variable kernels on the Hardy spaces Hp（Rn） and weak Hardy spaces WHP（Rn）.Moreover,by using the interpolation arguments,we can get some corresponding results for the above integral operators with variable kernels on Hardy-Lorentz spaces Hp,q（Rn） for all p 〈 q 〈 ∞.