A convolution property of the
Cantor–Lebesgue measure, II
Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 23-28
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
For $1\leq p,q \leq \infty $, we prove that the convolution operator generated by the Cantor–Lebesgue measure on the circle ${{\mathbb T}}$ is a contraction whenever it is bounded from $L^p ({{\mathbb T}} )$ to $L^q ({{\mathbb T}} )$. We also give a condition on $p$ which is necessary if this operator maps $L^p ({{\mathbb T}})$ into $L^2 ({{\mathbb T}} )$.
Keywords:
leq leq infty prove convolution operator generated cantor lebesgue measure circle mathbb contraction whenever bounded mathbb mathbb condition which necessary operator maps mathbb mathbb
Affiliations des auteurs :
Daniel M. Oberlin 1
@article{10_4064_cm97_1_3,
author = {Daniel M. Oberlin},
title = {A convolution property of the
{Cantor{\textendash}Lebesgue} measure, {II}},
journal = {Colloquium Mathematicum},
pages = {23--28},
year = {2003},
volume = {97},
number = {1},
doi = {10.4064/cm97-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm97-1-3/}
}
Daniel M. Oberlin. A convolution property of the Cantor–Lebesgue measure, II. Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 23-28. doi: 10.4064/cm97-1-3
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