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arXiv · 1907.12788

Properties of moduli of smoothness in $L_p(\mathbb{R}^d)$

Yurii Kolomoitsev·Sergey Tikhonov
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Abstract

In this paper, we discuss various basic properties of moduli of smoothness of functions from $L_p(\mathbb{R}^d)$, $0<p\le \infty$. In particular, complete versions of Jackson-, Marchaud-, and Ulyanov-type inequalities are given for the whole range of $p$. Moreover, equivalences between moduli of smoothness and the corresponding $K$-functionals and the realization concept are proved.

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Yurii Kolomoitsev, Sergey Tikhonov. 2019-07-30. Properties of moduli of smoothness in $L_p(\mathbb{R}^d)$. https://arxiv.org/abs/1907.12788

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