山西大学学报（自然科学版）2025，Vol.48Issue(6)：1113-1118,6.DOI:10.13451/j.sxu.ns.2024013
拟微分算子弱(1,1)估计的一个证明
A Proof of Weak(1,1)Estimates for Pseudodifferential Operators
摘要
Abstract
Pseudodifferential operators are one of the core research objects in modern harmonic analysis and they have important ap-plications in the theoretical study of partial differential equations.In this paper,we discuss the weak type endpoint estimates for pseu-dodifferential operators with symbols in Hörmander classes and get a sufficient condition such that these operators are of weak type(1,1)by employing the classical Calderón-Zygmund decomposition theory.Specifically,under the condition that the order of the symbol function m≤-(n+1)(1-ρ),these operators are bounded from Lebesgue spaces to weak Lebesgue spaces.This research enriches the boundedness theory of pseudodifferential operators.关键词
拟微分算子/奇异积分算子/弱(1,1)有界性估计/Calderón-Zygmund分解Key words
pseudodifferential operators/singular integral operators/estimates of weak type(1,1)/Calerón-Zygmund decomposition分类
数学引用本文复制引用
邓宇龙..拟微分算子弱(1,1)估计的一个证明[J].山西大学学报（自然科学版）,2025,48(6):1113-1118,6.基金项目
湖南省教育厅重点科研项目(21A0617) （21A0617）
