WEIGHTED ESTIMATES FOR DISCRETE ITERATED HARDY OPERATOR - Temirkhanova, A.; Sarsenaly, D.; Sarybai, M. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2022)
One of the most intensively studied topics in the theory of Hardy inequalities in recent years has been the estimation of iterated operators. Since these inequalities have found their application in the study of boundedness from a weighted Lebesgue space to a local Morrie-type space, as well as in the study of weighted bilinear Hardy type inequalities. The discrete case of iterated inequalities is an open problem. An inequality involving an iteration of a discrete Hardy operator is traditionally considered difficult to evaluate because it contains three independent weight sequences and three parameters in their different ratios. The aim of this paper is to obtain the necessary and sufficient conditions for the implementation of a discrete iterative Hardy inequality.