Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces

Kawasumi, Ryota; Nakai, Eiichi; Shi, Minglei

doi:10.48550/arxiv.2107.10553

Cited by 2 publications

(1 citation statement)

References 44 publications

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“…We will state the definitions of the Young function and the Orlicz space in Section 5. For the generalized fractional integral operator I ρ , see also [1,2,15,18,26,30,31,40] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group

Amagai¹,

Nakai

Sadasue

2023

Taiwanese J. Math.

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It is known that the fractional integral operator I α based on a symmetric Markovian semigroup with Varopoulos dimension d is bounded from L p to L q , if 0 < α < d, 1 < p < q < ∞ and −d/p + α = −d/q, like the usual fractional integral operator defined on the d dimensional Euclidean space. We introduce generalized fractional integral operators based on symmetric Markovian semigroups and extend the L p -L q boundedness to Orlicz spaces. We also apply the result to the semigroup associated with the diffusion process generated by the sub-Laplacian on the Heisenberg group. Moreover, we show necessary and sufficient conditions for the boundedness of the generalized fractional integral operator on the space of homogeneous type and apply them to the Heisenberg group.

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Section: Introductionmentioning

confidence: 99%

Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group

Amagai¹,

Nakai

Sadasue

2023

Taiwanese J. Math.

Self Cite

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Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces

Kawasumi¹,

Nakai²

2021

Preprint

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For the Hardy-Littlewood maximal and Calderón-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak Orlicz-Morrey spaces. To do this we show the weak-weak modular inequality. The Orlicz-Morrey space and its weak version contain weighted Orlicz, Morrey and Lebesgue spaces and their weak versions as special cases. Then we also get the boundedness for these function spaces as corollaries.

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Characterization of the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces

Cited by 2 publications

References 44 publications

Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group

Generalized Fractional Integral Operators Based on Symmetric Markovian Semigroups with Application to the Heisenberg Group

Weighted boundedness of the Hardy-Littlewood maximal and Calderón-Zygmund operators on Orlicz-Morrey and weak Orlicz-Morrey spaces

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