Sharp bounds for the spherical restriction Fourier transform in classical Lebesgue-Riesz and Grand Lebesgue spaces for ordinary and radial functions

2021/10/05 by M. R. Formica, Formica, M. R., E. Ostrovsky +3
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2110.02760

openalex publication_date 2021/10/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We derive bilateral estimates for the constants appearing in the Fourier transform restricted theorems on the Euclidean sphere for the ordinary and especially radial functions belonging to the Lebesgue-Riesz spaces as well as belonging to the Grand Lebesgue Spaces. We obtain an exact estimate for the norm of the restriction Fourier transform operator acting on the radial functions.

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