Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Besov spaces induced by doubling weights   Let $1\le p<\infty$, $0<q<\infty$ and $\nu$ be a two-sided doubling weight
satisfying
  $$\sup_{0\le
r<1}\frac{(1-r)^q}{\int_r^1\nu(t)\,dt}\int_0^r\frac{\nu(s)}{(1-s)^q}\,ds<\infty.$$
The weighted Besov space $\mathcal{B}_{\nu}^{p,q}$ consists of those $f\in H^p$
such that
  $$\int_0^1 \left(\int_{0}^{2\pi}
|f'(re^{i\theta})|^p\,d\theta\right)^{q/p}\nu(r)\,dr<\infty.$$ Our main result
gives a characterization for $f\in \mathcal{B}_{\nu}^{p,q}$ depending only on
$|f|$, $p$, $q$ and $\nu$. As a consequence of the main result and inner-outer
factorization, we obtain several interesting by-products. In particular, we
show the following modification of a classical factorization by F. and R.
Nevanlinna: If $f\in \mathcal{B}_{\nu}^{p,q}$, then there exist $f_1,f_2\in
\mathcal{B}_{\nu}^{p,q} \cap H^\infty$ such that $f=f_1/f_2$. In addition, we
give a sufficient and necessary condition guaranteeing that the product of
$f\in H^p$ and an inner function belongs to $\mathcal{B}_{\nu}^{p,q}$. Applying
this result, we make some observations on zero sets of
$\mathcal{B}_{\nu}^{p,p}$.

19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org