Extrapolation on function and modular spaces, and applications

Mingming Cao; Juan José Marín; José María Martell

doi:10.1016/j.aim.2022.108520

Extrapolation on function and modular spaces, and applications

Mingming Cao
, Juan José Marín
, José María Martell^*

^*Corresponding author for this work

CSIC

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

23 Scopus citations

Abstract

We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.

Original language	English
Article number	108520
Journal	Advances in Mathematics
Volume	406
DOIs	https://doi.org/10.1016/j.aim.2022.108520
State	Published - 17 Sep 2022
Externally published	Yes

Keywords

Banach function spaces
Dirichlet problem
Modular spaces
Muckenhoupt weights
Rubio de Francia extrapolation
Vector-valued inequalities

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10.1016/j.aim.2022.108520

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title = "Extrapolation on function and modular spaces, and applications",

abstract = "We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.",

keywords = "Banach function spaces, Dirichlet problem, Modular spaces, Muckenhoupt weights, Rubio de Francia extrapolation, Vector-valued inequalities",

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AU - Cao, Mingming

AU - Marín, Juan José

AU - Martell, José María

PY - 2022/9/17

Y1 - 2022/9/17

N2 - We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.

AB - We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.

KW - Banach function spaces

KW - Dirichlet problem

KW - Modular spaces

KW - Muckenhoupt weights

KW - Rubio de Francia extrapolation

KW - Vector-valued inequalities

UR - https://www.scopus.com/pages/publications/85132161232

U2 - 10.1016/j.aim.2022.108520

DO - 10.1016/j.aim.2022.108520

M3 - 文章

AN - SCOPUS:85132161232

SN - 0001-8708

VL - 406

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 108520

ER -

Extrapolation on function and modular spaces, and applications

Abstract

Keywords

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