Hormander Type Multipliers on Anisotropic Hardy Spaces

作     者：Jiao CHEN Liang HUANG 

作者机构：School of Mathematical SciencesChongqing Normal UniversityChongqing 401131P.R.China School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P.R.China 

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

年 卷 期：2019年第35卷第11期

页      面：1841-1853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 partly by NNSF of China(Grant No.11371056) supported by NNSF of China(Grant No.11801049) Technology Pro ject of Chongqing Education Committee(Grant No.KJQN201800514) 

主　　题：Hormander multiplier Littlewood-Paley’s inequality anisotropic Hardy space anisotropic Sobolev spaces 

摘      要：The main purpose of this paper is to establish, using the Littlewood–Paley–Stein theory(in particular, the Littlewood–Paley–Stein square functions), a Calderón–Torchinsky type theorem for the following Fourier multipliers on anisotropic Hardy spaces Hp(Rn;A) associated with expensive dilation A:■Our main Theorem is the following: Assume that m(ξ) is a function on Rn satisfying ■with s ζ--1(1/p-1/2). Then Tm is bounded from Hp(Rn;A) to Hp(Rn;A) for all 0 p ≤ 1 and ■where A* denotes the transpose of A. Here we have used the notations mj(ξ) = m(A*jξ)φ(ξ) and φ(ξ) is a suitable cut-off function on Rn, and Ws(A*) is an anisotropic Sobolev space associated with expansive dilation A* on Rn.