Lebesgue spaces norm estimates for fractional integrals and derivatives

TL;DR

This paper investigates the estimation of Lebesgue-Riesz and Grand Lebesgue norms for fractional integrals and derivatives within classical Lebesgue-Riesz and modified Besov spaces, providing new bounds and insights.

Contribution

It introduces novel norm estimation techniques for fractional calculus operators in Lebesgue and Besov spaces, expanding theoretical understanding.

Findings

Derived bounds for fractional integrals in Lebesgue spaces

Established norm estimates for fractional derivatives in Besov spaces

Extended classical results to Grand Lebesgue spaces

Abstract

We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.