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

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 s...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Amiran Gogatishvili, Opic, Bohumir, Tikhonov, Sergey, Trebels, Walter
Format: Article
Language:English
Subjects:
Function space
Inequalities
Interpolation
Smoothness
Online Access:Get full text
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Summary: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.
ISSN:2331-8422