Sharp weak bounds for discrete Hardy operator on discrete central Morrey spaces

Wei, Mingquan; Liu, Xiaoyu

doi:10.3934/math.2023250

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Xuebing Hao Baode LI and Shuai Yang1

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2023

2024

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Cited by 4 publications

(2 citation statements)

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“…In 2019, Gunawan and Schwanke [9] discussed the boundedness of discrete Riesz potentials on discrete Morrey spaces of arbitrary dimension as follows; more results for discrete Morrey spaces see [1,2,3,12,13,25].…”

Section: Xuebing Hao Baode LI and Shuai Yangmentioning

confidence: 99%

Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces

Hao,

Li,

Yang

2024

Ann. Funct. Anal.

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Let 0 < α < 1. We obtain the necessary and sufficient conditions for the boundedness of discrete fractional Hardy-Littlewood maximal operators M α on discrete weighted Lebesgue spaces. From this and a discrete variant of Whitney decomposition theorem, the necessary and sufficient conditions for the boundedness of the discrete Riesz potentials I α on discrete weighted Lebesgue spaces are discussed. As applications, the boundedness of I α on discrete weighted Morrey spaces is further obtained.

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Section: Xuebing Hao Baode LI and Shuai Yangmentioning

confidence: 99%

Estimates of discrete Riesz potentials on discrete weighted Lebesgue spaces

Hao,

Li,

Yang

2024

Ann. Funct. Anal.

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“…In addition, discrete Morrey spaces can be used to study the properties of discrete operators and the properties of the spaces themselves. For more results on discrete Morrey spaces, we lead the reader to [1,2,3,11,12,21].…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Zhao

2022

Anal.Math.Phys.

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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

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