Fourier inequalities in variable Lebesgue spaces

2026/07/17 by Rodrigo Cardeccia, Matías I. Caruso, Martin Mazzitelli +1
Mathematics · #math.CA

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Abstract

We study the boundedness of the Fourier transform on variable Lebesgue spaces. We obtain necessary conditions and, independently, sufficient conditions on the exponents p(⋅) and q(⋅) under which the inequality ‖f‖_q(⋅)≤ C‖f‖_p(⋅) holds for some constant C>0 and all f∈ L^p(⋅)(ℝ). As a byproduct, we improve some recent results of Saucedo and Tikhonov. Moreover, when p(x)→ 1 and q(x)→ +∞ as |x|→ +∞, we characterize the exponents for which the Fourier transform is bounded.

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