Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixed Moduli of Smoothness in $L_p$, $1<p<\infty$   In this paper we survey recent developments over the last 25 years on the
mixed fractional moduli of smoothness of periodic functions from $L_p$,
$1<p<\infty$. In particular, the paper includes monotonicity properties,
equivalence and realization results, sharp Jackson, Marchaud, and Ul'yanov
inequalities, interrelations between the moduli of smoothness, the Fourier
coefficients, and "angular" approximation. The sharpness of the results
presented is discussed.

25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat