Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hollenbeck-Verbitsky conjecture on best constant inequalities for
  analytic and co-analytic projections   \begin{abstract}
  In this paper we address the problem of finding the best constants in
inequalities of the form:
  $$ \|\big(|P_+f|^s+|P_-f|^s\big)^{\frac{1}{s}}\|_{L^p({\mathbb{T}})}\leq
A_{p,s} \|f\|_{L^p({\mathbb{T}})},$$ where $P_+f$ and $P_-f$ denote analytic
and co-analytic projection of a complex-valued function $f \in
L^p({\mathbb{T}}),$ for $p \geq 2$ and all $s>0$, thus proving
Hollenbeck-Verbitsky conjecture from \cite{HV.OTAA}. We also prove the same
inequalities for\\ $1<p\leq\frac{4}{3}$ and $s\leq \sec^2\frac{\pi}{2p}$ and
confirm that $s=\sec^2\frac{\pi}{2p}$ is the sharp cutoff for $s.$ The proof
uses a method of plurisubharmonic minorants and an approach of proving the
appropriate "elementary" inequalities that seems to be new in this topic.
  We show that this result implies best constants inequalities for the
projections on the real-line and half-space multipliers on $\mathbb{R}^n$ and
an analog for analytic martingales. A remark on an isoperimetric inequality for
harmonic functions in the unit disk is also given.
  \end{abstract}

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat