Lebesgue-Riesz norm estimates for fractional Laplace transform

TL;DR

This paper derives precise non-asymptotic bounds for the Lebesgue-Riesz and Grand Lebesgue space norms of the fractional Laplace transform, providing examples to demonstrate the bounds' sharpness.

Contribution

It introduces new bilateral norm estimates for the fractional Laplace transform in Lebesgue-Riesz and Grand Lebesgue spaces, with proofs of their optimality.

Findings

Established sharp bilateral norm inequalities for fractional Laplace transform.

Provided examples confirming the bounds' optimality.

Extended analysis to Grand Lebesgue spaces.

Abstract

We obtain in this short article the bilateral non-asymptotic estimations for the norm in Lebesgue-Riesz and bilateral Grand Lebesgue spaces of the so-called fractional Laplace integral transform. We give also examples to show the sharpness of these inequalities.