A convolution property of the Cantor–Lebesgue measure, II

Daniel M. Oberlin¹

¹ Department of Mathematics Florida State University Tallahassee, FL 32306-4510, U.S.A.

Colloquium Mathematicum, Tome 97 (2003) no. 1, pp. 23-28.

Résumé

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 $L^2 ({{\mathbb T}} )$.

Détail

DOI : 10.4064/cm97-1-3

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