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

• 作者: Yong DING Yao-ming NIU
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 187-208
• 页数: 22页
• 语种: 英文

摘要

For a function φ satisfying some suitable growth conditions,consider the following general disper-sive equation defined by{i?tu+φ((√-Δ)u=0,(x,t)∈Rn×R,(*)u(x,0)=f(x),f ∈ S(Rn),where φ(√-Δ)is a pseudo-differential operator with symbol φ(|ξ|).In the present paper,when the initial data f belongs to Sobolev space,we give the local and global weighted Lq estimate for the global maximal operator S**φ defined by S**φ f(x)=sup t∈R|St,φf(x)|,where St,φf(x)=(2π)-n ∫Rneix·ξ+itφ(|ξ|)(f)(ξ)dξis a formal solution of the equation(*).