Characterizations of weak reverse Hölder inequalities on metric measure spaces

Juha Kinnunen; Emma Karoliina Kurki; Carlos Mudarra

doi:10.1007/s00209-022-02976-y

Characterizations of weak reverse Hölder inequalities on metric measure spaces

Juha Kinnunen^*, Emma Karoliina Kurki, Carlos Mudarra

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

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Abstract

We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak A_∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt A_∞ weights that fail to hold for weak A_∞ weights.

Original language	English
Pages (from-to)	2269-2290
Journal	Mathematische Zeitschrift
Volume	301
Issue number	3
Early online date	17 Feb 2022
DOIs	https://doi.org/10.1007/s00209-022-02976-y
Publication status	Published - Jul 2022
MoE publication type	A1 Journal article-refereed

Funding

E.-K. Kurki has been funded by a young researcher’s grant from the Emil Aaltonen Foundation. C. Mudarra acknowledges financial support from the Academy of Finland.

Keywords

Maximal functions
Reverse Hölder inequalities
Weak Muckenhoupt weights

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10.1007/s00209-022-02976-yLicence: CC BY

Characterizations of weak reverse Hölder inequalities on metric measure spacesFinal published version, 309 KBLicence: CC BY

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title = "Characterizations of weak reverse H{\"o}lder inequalities on metric measure spaces",

abstract = "We present ten different characterizations of functions satisfying a weak reverse H{\"o}lder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak A∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt A∞ weights that fail to hold for weak A∞ weights.",

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author = "Juha Kinnunen and Kurki, \{Emma Karoliina\} and Carlos Mudarra",

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doi = "10.1007/s00209-022-02976-y",

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AU - Kurki, Emma Karoliina

AU - Mudarra, Carlos

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N2 - We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak A∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt A∞ weights that fail to hold for weak A∞ weights.

AB - We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak A∞ weights, which is a generalization of Muckenhoupt weights that allows for nondoubling weights. Although our main results are modeled after conditions that hold true for Muckenhoupt weights, we also discuss two conditions for Muckenhoupt A∞ weights that fail to hold for weak A∞ weights.

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KW - Reverse Hölder inequalities

KW - Weak Muckenhoupt weights

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ER -

Characterizations of weak reverse Hölder inequalities on metric measure spaces

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