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

Naoya Hatano, Masahiro Ikeda

Abstract

We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the Hardy-Hénon 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.

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

Abstract

We study the smoothing estimate for the heat semigroup which is related to the nonlinear term of the Hardy-Hénon 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.
Paper Structure (5 sections, 9 theorems, 32 equations)

This paper contains 5 sections, 9 theorems, 32 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem \ref{['thm:Mpq-wLs']}
  4. Remarks
  5. Proof of Lemma \ref{['lem:LM-Ia']}

Key Result

Theorem 1.2

Let $1<q\le p<\infty$, $1<s<\infty$ and $\gamma>0$, and assume that Then the following assertions hold :

Theorems & Definitions (16)

  • Definition 1.1
  • Theorem 1.2
  • Definition 2.1
  • Lemma 2.2: SDH20
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Theorem 2.5
  • Definition 4.1
  • Definition 4.2
  • ...and 6 more