Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems

Abstract

In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+). The results will be proved by employing the self-improving property of the discrete Ap-Muckenhoupt weights and the Marcinkiewicz Interpolation Theorem.

Boundedness of the fractional Hardy-Littlewood maximal operator on weighted Morrey spaces

“…When Z is restricted to Z + , Theorem 4.2 (ii) coincides with[16, Lemma 3]. In addition, Theorem 4.2 (ii) is proved by means of a discrete Calderón-Zygmund decomposition for weighted l 1 -sequences, while[16, Lemma 3] is proved via Yang inequality and Hardy operator.…”

“…On the other hand, it is very important to study weighted estimates for all kinds of discrete operators in harmonic analysis. On the discrete weighted l p spaces, in 2021, when Z is restricted to Z + , the boundedness of discrete Hardy-Littlewood maximal operators was obtained via Hardy operator by Saker and Agarwal [16]. For more studies of discrete weighted Lebesgue spaces, we refer the reader to [4,7,17,18].…”

Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces

“…In 2021, when Z is restricted to Z + , Saker-Agarwal [19] and Saker-Mahmoud [20] obtained the boundedness of the discrete Hardy-Littlewood maximal operators via Hardy operator on discrete weighted Lebesgue spaces. In addition, the discrete maximal operators and the discrete Riesz potentials have also been studied on discrete Morrey spaces in [9].…”

“…In 2023, we [10] introduce a discrete version of weighted Morrey spaces and showed the boundedness of the discrete Hardy-Littlewood maximal operator on discrete weighted Morrey spaces. Thus combining [16], [19], [20] and [9], we generate the following natural questions:…”