Boundedness of Hausdorff operators on the power weighted Hardy spaces

作     者：CHEN Jie-cheng HE Shao-yong ZHU Xiang-rong 

作者机构：Department of Mathematics Zhejiang Normal University Jinhua 321004 China 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2017年第32卷第4期

页      面：462-476页

核心收录：

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

基　　金：Supported by the National Natural Science Foundation of China(11671363 11471288) 

主　　题：Hausdorff operator Hardy space power weight 

摘      要：In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;（R;） （ -1 ≤α≤0）, defined by H;f（x）=∫R;Φ（u）f(A（u）x)du,where Φ∈L;oc;（R;）,A（u） = (α;（u）);is a 2×2 matrix, and each α;is a *** obtain that HΦ,A is bounded from H;（R;） （ -1≤α≤0） to itself, if∫R2|Φ（u）‖det A;（u）|‖A（u）‖;ln(1+‖A;（u）‖;/|det A;（u）|)du∞.This result improves some known theorems, and in some sense it is sharp.