Estimates for the wave equation on $\beta$-dimensional spaces of measures

TL;DR

This paper develops refined fixed-time estimates for wave multipliers on measure spaces with fractional dimensions, leading to improved understanding of wave equations with measure data.

Contribution

It introduces Miyachi-Peral-type estimates for wave multipliers on 5-dimensional measure spaces, refining previous Hardy space estimates and applying them to wave equations with measure data.

Findings

Refined fixed-time estimates for wave multipliers on 5-dimensional measure spaces

Improved bounds for the wave equation with measure data

Enhanced understanding of wave behavior on fractal-like measure spaces

Abstract

In this paper, we establish Miyachi-Peral-type fixed-time estimates for wave multipliers acting on $\beta$-dimension stable spaces of measures. Our estimates give a refinement of known estimates for the Hardy space. From these bounds, we deduce corresponding estimates for the wave equation with measure data.