Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of moduli of smoothness in $L_p(\mathbb{R}^d)$   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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The categories of this paper are: supr-con
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci