A unified approach to inequalities for K-functionals and moduli of smoothness

TL;DR

This paper introduces a unified method using Holmstedt formulas to derive inequalities for smoothness measures and K-functionals across various Banach spaces, especially Lorentz spaces.

Contribution

It presents a novel unified approach to inequalities for K-functionals and moduli of smoothness in rearrangement invariant Banach spaces.

Findings

Derived new inequalities for moduli of smoothness.

Established estimates for K-functionals in Lorentz spaces.

Unified approach simplifies analysis across different spaces.

Abstract

The paper provides a detailed study of crucial inequalities for smoothness and interpolation characteristics in rearrangement invariant Banach function spaces. We present a unified approach based on Holmstedt formulas to obtain these estimates. As examples, we derive new inequalities for moduli of smoothness and K-functionals in various Lorentz spaces.