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

2023/07/11 by Gogatishvili, Amiran, Opic, Bohumir, Tikhonov, Sergey +1 · 2 citations
#41A17 #46B70 #46E30 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2307.05124

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.

Cited by

• Interpolation of classical Lorentz spaces measuring oscillation
• Fractional Bessel-Sobolev and Bessel B-potential spaces

Related

• Real interpolation with weighted rearrangement invariant Banach function spaces
• Real Interpolation method, Lorentz spaces and refined Sobolev inequalities
• Wirtinger-type inequalities for some rearrangement invariant spaces
• Gagliardo-Nirenberg Inequality for rearrangement-invariant Banach function spaces
• Multidimensional rearrangement and Lorentz spaces