Smoothing estimate for the heat semigroup with a homogeneous weight on Morrey spaces

TL;DR

This paper investigates smoothing estimates for the heat semigroup with homogeneous weights on Morrey spaces, improving previous results by employing advanced function space techniques to better understand nonlinear heat equations.

Contribution

It provides an improved smoothing estimate for the heat semigroup on Morrey spaces, extending prior work with more refined analytical tools.

Findings

Enhanced smoothing estimates for the heat semigroup on Morrey spaces

Application to nonlinear Hardy-Hénon parabolic equations

Utilization of weak Lebesgue and Lorentz spaces for sharper results

Abstract

We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the Hardy-H\'enon parabolic equation on Morrey spaces. This result is improvement of \cite[Proposition 3.3]{Tayachi20}, which is proved by using weak Lebesgue and Lorentz spaces.