Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improving Beckner's bound via Hermite functions   We obtain an improvement of the Beckner's inequality $\| f\|^{2}_{2}
-\|f\|^{2}_{p} \leq (2-p) \| \nabla f\|_{2}^{2}$ valid for $p \in [1,2]$ and
the Gaussian measure. Our improvement is essential for the intermediate case $p
\in (1,2)$, and moreover, we find the natural extension of the inequality for
any real $p$.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph