$L^p -L^q$ boundedness of Fourier multipliers on quantum Euclidean spaces

Autor:	Ruzhansky, M., Shaimardan, S., Tulenov, K.
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis
Druh dokumentu:	Working Paper
Popis:	In this paper, we study Fourier multipliers on quantum Euclidean spaces and obtain results on their $L^p -L^q$ boundedness. On the way to get these results, we prove Paley, Hausdorff-Young-Paley, and Hardy-Littlewood inequalities on the quantum Euclidean space. As applications, we establish the $L^p -L^q$ estimate for the heat semigroup and Sobolev embedding theorem on quantum Euclidean spaces. We also obtain quantum analogues of the logarithmic Sobolev and Nash type inequalities. Comment: 27
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.00657 Zobrazit plný text záznamu View this record from Arxiv