The Martingale Hardy Type Inequalities for Dyadic Derivative and Integral

作     者：JianYingNIE Xing Guo Nie GUO Wei LOU 

作者机构：Institute of Near Sensing Technique with Millimeter Wave & Optical WaveNanjing University of Science ~ Technology Nanjing 210094 P. R. China 

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

年 卷 期：2005年第21卷第6期

页      面：1465-1474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：the Preliminary Research Foundation of National Defense (No,002,2BQ) the Foundation of Fuzhou University (No.0030824649) 

主　　题：martingale Hardy space dyadic derivative dyadic integral Walsh-Fejer kernels p-atom,quasi-local operator 

摘      要：Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.