The Fourier transform in Lebesgue spaces

2023/09/04 by Talvila, Erik · 1 citation
#46B04 #46B04 (Secondary) 26A42 #46F10 (Primary) 26A42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 42A38

paper · doi:10.48550/arxiv.2309.01699

Abstract

For each f∈ L^p(\mathbb R) (1≤ p<∞) it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each p a norm is defined so that the space Fourier transforms is isometrically isomorphic to L^p(\mathbb R). There is an exchange theorem and inversion in norm.

Cited by

• The Fourier transform in variable exponent Lebesgue spaces

Related

• The Fourier transform in variable exponent Lebesgue spaces
• The Fourier transform with Henstock--Kurzweil and continuous primitive integrals
• The Fourier transform on Rearrangement-Invariant Spaces
• Quantitative Non-Compactness Properties of the Fourier Transform on Optimal Spaces
• Mapping properties of Fourier transforms, revisited