Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp $L^p$ estimates for discrete second order {R}iesz transforms   We show that multipliers of second order Riesz transforms on products of
discrete abelian groups enjoy the $L^{p} $ estimate $p^{\ast} -1$, where
$p^{\ast} = \max \{ p,q \}$ and $p$ and $q$ are conjugate exponents. This
estimate is sharp if one considers all multipliers of the form $\sum_i
\sigma_{i} R_{i} R^{\ast}_{i}$ with $| \sigma_{i} | \leqslant 1$ and infinite
groups. In the real valued case, we obtain better sharp estimates for some
specific multipliers, such as $\sum_{i} \sigma_{i} R_{i} R^{\ast}_{i}$ with $0
\leqslant \sigma_{i} \leqslant 1$. These are the first known precise $L^{p} $
estimates for discrete Calder\'on-Zygmund operators.

35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio