Properties of moduli of smoothness in $L_p(\mathbb{R}^d)$
Classical Analysis and ODEs
2020-03-26 v3
Abstract
In this paper, we discuss various basic properties of moduli of smoothness of functions from , . In particular, complete versions of Jackson-, Marchaud-, and Ulyanov-type inequalities are given for the whole range of . Moreover, equivalences between moduli of smoothness and the corresponding -functionals and the realization concept are proved.
Keywords
Cite
@article{arxiv.1907.12788,
title = {Properties of moduli of smoothness in $L_p(\mathbb{R}^d)$},
author = {Yurii Kolomoitsev and Sergey Tikhonov},
journal= {arXiv preprint arXiv:1907.12788},
year = {2020}
}