The Fourier transform in variable exponent Lebesgue spaces
Abstract
Abstract In this work we define a Fourier transform for each $$f\in L^{p(\cdot )}({{\,\mathrm{\mathbb {R}}\,}})$$ f ∈ L p ( · ) ( R ) , for a large class of exponent functions $$p(\cdot )$$ p ( · ) , as the distributional derivative of a Hölder continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to $$L^{p(\cdot )}({{\,\mathrm{\mathbb {R}}\,}})$$ L p ( · ) ( R ) . We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Holomorphic and Operator Theory
Publication details
- Journal / source
- Advances in Operator Theory
- Volume
- 11
- Issue
- 4
- Publication date
- 13 August 2026
- Language
- EN