Besov and Hölder spaces on spaces of homogeneous type

Yongshen Han; Ming Yi Lee; Chin Cheng Lin

doi:10.4064/sm180925-17-9

Besov and Hölder spaces on spaces of homogeneous type

Yongshen Han, Ming Yi Lee, Chin Cheng Lin

Department of Mathematics

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

Abstract

We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding Hölder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding Hölder spaces. As an application, we show that Monge–Ampère singular integral operators are bounded on these spaces.

Original language	English
Pages (from-to)	219-263
Number of pages	45
Journal	Studia Mathematica
Volume	255
Issue number	3
DOIs	https://doi.org/10.4064/sm180925-17-9
State	Published - 2020

Keywords

Besov spaces
Hölder spaces
Monge–Ampère singular integral operators

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10.4064/sm180925-17-9

Bmo Spaces Associated with a Family of General Sets(3/3)
Lin, C.
1/08/19 → 31/07/21
Project: Research
The Atomic Decomposition of Flag Hardy Spaces(1/2)
Lee, M.
1/08/19 → 31/07/20
Project: Research

Cite this

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abstract = "We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding H{\"o}lder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding H{\"o}lder spaces. As an application, we show that Monge–Amp{\`e}re singular integral operators are bounded on these spaces.",

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AU - Lee, Ming Yi

AU - Lin, Chin Cheng

N1 - Publisher Copyright: © Instytut Matematyczny PAN, 2020.

PY - 2020

Y1 - 2020

N2 - We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding Hölder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding Hölder spaces. As an application, we show that Monge–Ampère singular integral operators are bounded on these spaces.

AB - We establish a theory of Besov spaces associated with a family of quasi-metric balls under only the doubling condition on the measure. We introduce the corresponding Hölder spaces as well, and show that the duals of some Besov spaces defined here are equivalent to the corresponding Hölder spaces. As an application, we show that Monge–Ampère singular integral operators are bounded on these spaces.

KW - Besov spaces

KW - Hölder spaces

KW - Monge–Ampère singular integral operators

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M3 - 期刊論文

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JO - Studia Mathematica

JF - Studia Mathematica

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ER -

Besov and Hölder spaces on spaces of homogeneous type

Abstract

Keywords

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Projects

Bmo Spaces Associated with a Family of General Sets(3/3)

The Atomic Decomposition of Flag Hardy Spaces(1/2)

Cite this