On the mutipliers of the Figá-Talamanca Herz algebra

Document Type : Dedicated to Prof. A. T.-M. Lau


MA A1 345 (B^atiment MA) Station 8 CH-1015 Lausanne.


Let $G$ be a locally compact group and $p,q \in \mathbb{R}$ with $p>1, \hskip2pt p\not =2$ and $q$ between $2$ and $p$ (if $p<2$ then $p<q<2,$ if $p>2$ then $2<q<p$.) The main result of the paper is that $ A_{q}(G)$ multiplies $A_p(G),$ more precisely we show that the Banach algebra $A_p(G)$ is a Banach module on $A_q(G).$


Main Subjects

[1] A. Derighetti, Convolution Operators on Groups, Lecture Notes of the Unione Matematica Italiana 11, Springer-Verlag Berlin Heidelberg, 2011.
[2] A. Derighetti, Survey on the Fig_a -Talamanca Herz algebra,  Mathematics 2019, 7(8) 660; https: // doi. org/3390/ math7080660 .
[3] C. Herz, The theory of p-spaces with an application to convolution operators, Trans. Am. Math. 154 (1971), 69--82.
[4] C. Herz and N. Riviere, Estimates for translation -invariant operators on spaces with mixed norms, Stud. Math. XLIV (1972), 511--515