Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Poisson integral and sharp estimates for harmonic and
  biharmonic functions in the half-space   A representation for the sharp coefficient in a pointwise estimate for the
gradient of a generalized Poisson integral of a function $f$ on ${\mathbb
R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is
assumed that the kernel of the integral depends on the parameters $\alpha$ and
$\beta$. The explicit formulas for the sharp coefficients are found for the
cases $p=1$, $p=2$ and for some values of $\alpha , \beta$ in the case
$p=\infty$. Conditions ensuring the validity of some analogues of the
Khavinson's conjecture for the generalized Poisson integral are obtained. The
sharp estimates are applied to harmonic and biharmonic functions in the
half-space.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas