Fourier multipliers and their applications to PDE on the quantum Euclidean space

In this work, we present some applications of the Lp-Lq boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we establish Lp-Lq norm estimates for solutions of heat, wave, and Schrödinger type equations with Caputo fractional derivative in th...

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Published inNonlinear differential equations and applications Vol. 32; no. 5
Main Authors Ruzhansky, Michael, Shaimardan, Serikbol, Tulenov, Kanat
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.09.2025
Subjects
Euclidean geometry
Multipliers
Wave equations
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Summary:In this work, we present some applications of the Lp-Lq boundedness of Fourier multipliers to PDEs on the noncommutative (or quantum) Euclidean space. More precisely, we establish Lp-Lq norm estimates for solutions of heat, wave, and Schrödinger type equations with Caputo fractional derivative in the case 1<p≤2≤q<∞. Moreover, we obtain well-posedness of nonlinear heat and wave equations on the noncommutative Euclidean space.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-025-01067-1