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

Abstract

In this paper, we introduce a discrete version of weighted Morrey spaces, and discuss the inclusion relations of these spaces. In addition, we obtain the boundedness of discrete weighted Hardy-Littlewood maximal operators on discrete weighted Lebesgue spaces by establishing a discrete Calderón-Zygmund decomposition for weighted l 1 -sequences. Furthermore, the boundedness of discrete Hardy-Littlewood maximal operators on discrete weighted Morrey spaces is established. Definition 1.2. Let x = {x(k)} k∈Z ⊂ R be a sequence. The discrete Hardy-Littlewood maximal operator M is defined by Mx(m) := sup N ∈N

Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces

“…Similar to the definition of discrete weight A(p, q)(Z) (1 < p, q < ∞), replacing Z by N, we can also give the definition of discrete weight A(p, q)(N). Particularly, if ω ∈ A(p, q)(N), then ω(•) := ω(|•|) ∈ A(p, q)(Z) and its proof is similar to that of [10,Proposition 2.11].…”

“…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:…”