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

Franka Baaske; Romaric Kana Nguedia; Hans-Jürgen Schmeißer; Franka Baaske; Romaric Kana Nguedia; Hans-Jürgen Schmeißer

doi:10.3934/math.20241536

AIMS Mathematics

2024, Volume 9, Issue 11: 31962-31984. doi: 10.3934/math.20241536

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

1.
University of Applied Sciences Mittweida, Faculty Applied Computer Sciences & Biosciences, Technikumplatz 17, 09648 Mittweida, Germany
2.
Friedrich Schiller University Jena, Faculty of Mathematics and Computer Sciences, Ernst-Abbe Platz 2, 07743 Jena, Germany

Received: 29 August 2024 Revised: 14 October 2024 Accepted: 24 October 2024 Published: 11 November 2024
MSC : 46E35, 46E30, 20M15, 41A30

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.
- Morrey smoothness spaces of Besov and Triebel-Lizorkin type,
- caloric smoothing,
- wavelets,
- molecules,
- fractional Gauss-Weierstrass semi-group
Citation: Franka Baaske, Romaric Kana Nguedia, Hans-Jürgen Schmeißer. Smoothing properties of the fractional Gauss-Weierstrass semi-group in Morrey smoothness spaces[J]. AIMS Mathematics, 2024, 9(11): 31962-31984. doi: 10.3934/math.20241536

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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.

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