Email this article On maximizers of a convolution operator in $L_p$-spaces
- Authors: Kalachev G.V.1, Sadov S.Y.2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Issue: Vol 210, No 8 (2019)
- Pages: 67-86
- Section: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/142374
- DOI: https://doi.org/10.4213/sm9099
- ID: 142374
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Abstract
The paper is concerned with convolution operators in $\mathbb R^d$, whose kernels are in $L_q$, which act from $L_p$ into $L_s$, where $1/p+1/q=1+1/s$. It is shown that for $1< q,p,s< \infty$ there exists a maximizer (a function with $L_p$-norm $1$) at which the supremum of the $s$-norm of the convolution is attained. A special analysis is carried out for the cases in which one of the exponents $q,p$, or $s$ is $1$ or $\infty$.
Bibliography: 12 titles.
About the authors
Gleb Vyacheslavovich Kalachev
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Author for correspondence.
Email: gleb.Kalachev@yandex.ru
Candidate of physico-mathematical sciences, Scientific Employee
Sergey Yur'evich Sadov
Email: serge.sadov@gmail.com
Candidate of physico-mathematical sciences, no status
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