General maximal operators and the reverse Hölder classes

Saito, Hiroki; Tanaka, Hitoshi

doi:10.5186/aasfm.2017.4227

Cited by 2 publications

(1 citation statement)

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“…Some of the theory has been adapted into metric spaces by Kinnunen-Shukla in [14,15]. Saito-Tanaka [21] consider maximal operators and reverse Hölder classes in R n with respect to general base of open sets. Finally, we refer to [11] for a visual scheme and many more classical references.…”

Section: Introductionmentioning

confidence: 99%

Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces

Kurki¹

2022

Preprint

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The natural maximal and minimal functions commute pointwise with the logarithm on A∞. We use this observation to characterize the spaces A1 and RH∞ on metric measure spaces with a doubling measure. As the limiting cases of Muckenhoupt Ap and reverse Hölder classes, respectively, their behavior is remarkably symmetric. On general metric measure spaces, an additional geometric assumption is needed in order to pass between Ap and reverse Hölder descriptions. Finally, we apply the characterization to give simple proofs of several known properties of A1 and RH∞, including a refined Jones factorization theorem. In addition, we show a boundedness result for the natural maximal function.

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Section: Introductionmentioning

confidence: 99%

Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces

Kurki¹

2022

Preprint

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Limiting Conditions of Muckenhoupt and Reverse Hölder Classes on Metric Measure Spaces

Kurki

2023

Results Math

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The natural maximal and minimal functions commute pointwise with the logarithm on $$A_\infty $$ A ∞ . We use this observation to characterize the spaces $$A_1$$ A 1 and $$RH_\infty $$ R H ∞ on metric measure spaces with a doubling measure. As the limiting cases of Muckenhoupt $$A_p$$ A p and reverse Hölder classes, respectively, their behavior is remarkably symmetric. On general metric measure spaces, an additional geometric assumption is needed in order to pass between $$A_p$$ A p and reverse Hölder descriptions. Finally, we apply the characterization to give simple proofs of several known properties of $$A_1$$ A 1 and $$RH_\infty $$ R H ∞ , including a refined Jones factorization theorem. In addition, we show a boundedness result for the natural maximal function.

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General maximal operators and the reverse Hölder classes

Cited by 2 publications

References 23 publications

Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces

Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces

Limiting Conditions of Muckenhoupt and Reverse Hölder Classes on Metric Measure Spaces

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