$l^{p}-L^{q}$ 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.