Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On moduli of smoothness with Jacobi weights   The main purpose of this paper is to introduce moduli of smoothness with
Jacobi weights $(1-x)^\alpha(1+x)^\beta$ for functions in the Jacobi weighted
$L_p[-1,1]$, $0<p\le \infty$, spaces. These moduli are used to characterize the
smoothness of (the derivatives of) functions in the weighted $L_p$ spaces. If
$1\le p\le\infty$, then these moduli are equivalent to certain weighted
$K$-functionals (and so they are equivalent to certain weighted Ditzian-Totik
moduli of smoothness for these $p$), while for $0<p<1$ they are equivalent to
certain "Realization functionals".

21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an