Maximal operators of pseudo-differential operators with rough symbols  

作　　者：Ramla Benhamoud ZHU Xiang-rong 

机构地区：[1]School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2024年第1期174-180,共7页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11871436,12071437)。

摘　　要：Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

关 键 词：pseudo-differential operator rough Hormander class H-L maximal operator 

分 类 号：O177[理学—数学]