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arXiv · 2101.03416

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

Vishvesh Kumar·Michael Ruzhansky
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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.

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Vishvesh Kumar, Michael Ruzhansky. 2021-01-09. $L^p$-$L^q$ boundedness of $(k, a)$-Fourier multipliers with applications to Nonlinear equations. https://doi.org/10.1093/imrn%2Frnab256

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