Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted inequalities for discrete iterated kernel operators   We develop a new method that enables us to solve the open problem of
characterizing discrete inequalities for kernel operators involving suprema.
More precisely, we establish necessary and sufficient conditions under which
there exists a positive constant $C$ such that \begin{equation*}
  \Bigg(\sum_{n\in\mathbb{Z}}\Bigg(\sum_{i=-\infty}^n {U}(i,n) a_i\Bigg)^{q}
{w}_n\Bigg)^{\frac{1}{q}}
  \le C \Bigg(\sum_{n\in\mathbb{Z}}a_n^p {v}_n\Bigg)^{\frac{1}{p}}
\end{equation*} holds for every sequence of nonnegative numbers
$\{a_n\}_{n\in\mathbb{Z}}$ where $U$ is a kernel satisfying certain regularity
condition, $0 < p,q \leq \infty$ and $\{v_n\}_{n\in\mathbb{Z}}$ and
$\{w_n\}_{n\in\mathbb{Z}}$ are fixed weight sequences. We do the same for the
inequality \begin{equation*}
  \Bigg( \sum_{n\in\mathbb{Z}} w_n \Big[ \sup_{-\infty<i\le n} U(i,n)
\sum_{j=-\infty}^{i} a_j \Big]^q \Bigg)^{\frac{1}{q}}
  \le C \Bigg( \sum_{n\in\mathbb{Z}} a_n^p v_n \Bigg)^{\frac{1}{p}}.
\end{equation*} We characterize these inequalities by conditions of both
discrete and continuous nature.

37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg