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Research Article | Open Access

Smoothing properties of the fractional Gauss-Weierstrass semi-group in Morrey smoothness spaces

Franka Baaske1( ), Romaric Kana Nguedia2, Hans-Jürgen Schmeißer2
University of Applied Sciences Mittweida, Faculty Applied Computer Sciences & Biosciences, Technikumplatz 17, 09648 Mittweida, Germany
Friedrich Schiller University Jena, Faculty of Mathematics and Computer Sciences, Ernst-Abbe Platz 2, 07743 Jena, Germany
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Abstract

In this paper we derive caloric smoothing estimates in Morrey smoothness spaces using decomposition techniques by means of wavelets and molecules. Our new estimate extends results for Gauss-Weierstrass, Cauchy-Poisson and fractional Gauss-Weierstrass semigroups.

Keywords

Morrey smoothness spaces of Besov and Triebel-Lizorkin typecaloric smoothingwaveletsmoleculesfractional Gauss-Weierstrass semi-group
CLC number: 46E35, 46E30, 20M15, 41A30

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 31962-31984
DOI: 10.3934/math.20241536

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Cite this article:
Baaske F, Nguedia RK, Schmeißer H-J. Smoothing properties of the fractional Gauss-Weierstrass semi-group in Morrey smoothness spaces. AIMS Mathematics, 2024, 9(11): 31962-31984. https://doi.org/10.3934/math.20241536

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Received: 29 August 2024
Revised: 14 October 2024
Accepted: 24 October 2024
Published: 11 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)