$l^p-L^q$ boundedness of sequence-to-function Hardy-Littlewood-Pólya-type operators

Abstract

In this paper we deal with the boundedness of certain generalized sequence-to-function Hardy-Littlewood-Pólya-type operators. We completely characterize the $l^p-L^q$ boundedness of these operators for all $(p,q)\in [1,\infty ]\times [1,\infty ]$. These results complement some previous results in the literature. Our method relies on the ideas of generalized Schur's tests developed by Okikiolu, Sinnamon, Tao and Zhao.

26 pages