Maximal multipliers on compact manifolds without boundary

TL;DR

This paper extends the Hormander-Mihklin multiplier theorem to maximal multipliers on compact manifolds without boundary, utilizing wave kernels and detailed analysis of remainder terms.

Contribution

It introduces a new approach to maximal multipliers on compact manifolds by analyzing wave kernels and remainder terms, expanding the multiplier theorem framework.

Findings

Established maximal multiplier bounds on compact manifolds without boundary.

Developed techniques for handling remainder terms in wave kernel analysis.

Provided additional insights into wave kernel behavior on compact manifolds.

Abstract

Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms and find an additional information on the wave kernels.