Sharp estimates for module of continuity of fractional integrals and derivatives

TL;DR

This paper provides precise bilateral estimates for the continuity modulus of fractional integrals and derivatives within classical Lebesgue-Riesz spaces, enhancing understanding of their regularity properties.

Contribution

It introduces sharp bilateral estimates for the module of continuity of fractional integrals and derivatives in Lebesgue-Riesz spaces, advancing the theoretical framework.

Findings

Derived bilateral estimates for fractional integrals

Established sharp bounds for fractional derivatives

Enhanced understanding of regularity in Lebesgue-Riesz spaces

Abstract

We derive the bilateral estimates for the module of continuity of the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces.