What question did this study set out to answer?

Define a generalized Fourier transform operator for functions in variable exponent Lebesgue spaces and establish its structural properties.

August 15, 2026Advances in Operator TheoryOpen Access

The Fourier transform in variable exponent Lebesgue spaces

View Full Paper

Ask AI

Bookmark

Define a generalized Fourier transform operator for functions in variable exponent Lebesgue spaces and establish its structural properties.
Defined the Fourier transform for functions in variable exponent Lebesgue spaces as the distributional derivative of a Hölder continuous function.
Constructed a specialized norm on the resulting space of transformed functions to evaluate topological equivalence and operator behavior.
Demonstrated that the space of constructed Fourier transforms is isometrically isomorphic to the variable exponent space.
Proved key harmonic analysis properties for the transform, including norm inversion and an exchange theorem.

Discussion

No takes yet. Share an insight, caveat, or question.

Implication

Theoretical study defines a Fourier transform in variable exponent Lebesgue spaces, demonstrating isometric isomorphism and norm inversion properties.

Cite This Study

Kowacs et al. (2026) studied this question.

synapsesocial.com/papers/6a80194675c2e31742c85570 https://doi.org/10.1007/s43036-026-00526-5

View Full Paper

Ask AI

Bookmark

Implication

Theoretical study defines a Fourier transform in variable exponent Lebesgue spaces, demonstrating isometric isomorphism and norm inversion properties.

The Fourier transform in variable exponent Lebesgue spaces

Key Points

Discussion

Implication

Cite This Study

The Fourier transform in variable exponent Lebesgue spaces

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider