Characterizations of parabolic Muckenhoupt classes

Juha Kinnunen; Kim Myyryläinen

doi:10.1016/j.aim.2024.109612

Characterizations of parabolic Muckenhoupt classes

Juha Kinnunen
, Kim Myyryläinen^*

^*Corresponding author for this work

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

5 Citations (Scopus)

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Abstract

This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of p-Laplace type. The main results include characterizations for the limiting parabolic A_∞ and A₁ classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calderón–Zygmund decompositions, covering and chaining arguments appear in the proofs.

Original language	English
Article number	109612
Journal	Advances in Mathematics
Volume	444
DOIs	https://doi.org/10.1016/j.aim.2024.109612
Publication status	Published - May 2024
MoE publication type	A1 Journal article-refereed

Keywords

Doubly nonlinear equation
One-sided weights
Parabolic maximal functions
Parabolic Muckenhoupt weights

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SCI_Kinnunen_etal_Advances_in_Mathematics_2024Final published version, 667 KBLicence: CC BY

Cite this

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title = "Characterizations of parabolic Muckenhoupt classes",

abstract = "This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of p-Laplace type. The main results include characterizations for the limiting parabolic A∞ and A1 classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calder{\'o}n–Zygmund decompositions, covering and chaining arguments appear in the proofs.",

keywords = "Doubly nonlinear equation, One-sided weights, Parabolic maximal functions, Parabolic Muckenhoupt weights",

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AU - Myyryläinen, Kim

PY - 2024/5

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N2 - This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of p-Laplace type. The main results include characterizations for the limiting parabolic A∞ and A1 classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calderón–Zygmund decompositions, covering and chaining arguments appear in the proofs.

AB - This paper extends and complements the existing theory for the parabolic Muckenhoupt weights motivated by one-sided maximal functions and a doubly nonlinear parabolic partial differential equation of p-Laplace type. The main results include characterizations for the limiting parabolic A∞ and A1 classes by applying an uncentered parabolic maximal function with a time lag. Several parabolic Calderón–Zygmund decompositions, covering and chaining arguments appear in the proofs.

KW - Doubly nonlinear equation

KW - One-sided weights

KW - Parabolic maximal functions

KW - Parabolic Muckenhoupt weights

UR - https://www.scopus.com/pages/publications/85188422507

U2 - 10.1016/j.aim.2024.109612

DO - 10.1016/j.aim.2024.109612

M3 - Article

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SN - 0001-8708

VL - 444

JO - Advances in Mathematics

JF - Advances in Mathematics

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ER -

Characterizations of parabolic Muckenhoupt classes

Abstract

Keywords

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