A convolution property of the Cantor–Lebesgue measure, II
Volume 97 / 2003
Colloquium Mathematicum 97 (2003), 23-28
MSC: Primary 42A45.
DOI: 10.4064/cm97-1-3
Abstract
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 $L^2 ({{\mathbb T}} )$.
