Weighted Estimates for a Class of Global Maximal Operators Associated with Dispersive Equation  

作　　者：Yong DING Yao-ming NIU 

机构地区：[1]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems(BNU),Ministry of Education,Beijing 100875,China [2]Faculty of Mathematics,Baotou Teachers’College of Inner Mongolia University of Science and Technology,Baotou 014030,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第1期187-208,共22页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11871096,12071473,11661061,11761054);by the Natural Science Foundation of Inner Mongolia(Nos.2019MS01003,2021MS01001);Inner Mongolia University scientific research projects(Nos.NJZY19186,NJZZ21050)。

摘　　要：For a function Ф satisfying some suitable growth conditions,consider the following general dispersive equation defined by{i■tu+Ф(√-△)u=0,u(x,0)=f(x),(x,t)∈R^(n)× R,f∈S(R^(n) where Ф(√-△)is a pseudo-differential operator with symbol Ф(|ξ|).In the present paper,when the initial data f belongs to Sobolev space,we give the local and global weighted L^(q) estimate for the global maximal operator S^(**)Ф defined by S^(**)Фf(x)=sup_(t∈R)|S_(t,Ф)f(x)|,where S_(t,Ф)f(x)=(2π)^(-n)∫_(R^(n)e^(ix·ζ+itФ(|ζ+|)f(ζ)dζ is a formal solution of the equation(*).

关 键 词：global maximal operator weighted estimate pseudo-differential operator dispersive equation 

分 类 号：O175[理学—数学]