L^p-L^q boundedness of (k, a)-Fourier multipliers with applications to Nonlinear equations

2021/01/31 by Vishvesh Kumar, Michael Ruzhansky
Mathematics · #math.FA #math.AP #msc:42B10 #msc:42B37 #msc:42B15 #msc:33C45

paper · pdf · doi:10.1093/imrn/rnab256

20 pages. arXiv admin note: text overlap with arXiv:2108.01146

arxiv created 2021/10/21 · arxiv updated 2021/10/22

Abstract

The (k,a)-generalised Fourier transform is the unitary operator defined using the a-deformed Dunkl harmonic oscillator.The main aim of this paper is to prove L^p-L^q boundedness of (k, a)-generalised Fourier multipliers. To show the boundedness we first establish Paley inequality and Hausdorff-Young-Paley inequality for (k, a)-generalised Fourier transform. We also demonstrate applications of obtained results to study the well-posedness of nonlinear partial differential equations.

Citations

• L^p-L^q Multipliers on commutative hypergroups