Geodesic
On maximizers of a convolution operator in $L_p$-spaces
Sbornik. Mathematics, Tome 210 (2019) no. 8, pp. 1129-1147 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 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.
Keywords: Young inequality, existence of an extremal function, tight sequence, concentration compactness.
Mots-clés : convolution 
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G. V. Kalachev; S. Yu. Sadov. On maximizers of a convolution operator in $L_p$-spaces. Sbornik. Mathematics, Tome 210 (2019) no. 8, pp. 1129-1147. http://geodesic.mathdoc.fr/item/SM_2019_210_8_a2/

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