Parabolic BMO and the forward-in-time maximal operator

Olli Saari

doi:10.1007/s10231-018-0733-0

Parabolic BMO and the forward-in-time maximal operator

Olli Saari^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

4 Citations (Scopus)

Abstract

We study if the parabolic forward-in-time maximal operator is bounded on parabolic (Formula presented.). It turns out that for non-negative functions the answer is positive, but the behavior of sign-changing functions is more delicate. The class parabolic (Formula presented.) and the forward-in-time maximal operator originate from the regularity theory of nonlinear parabolic partial differential equations. In addition to that context, we also study the question in dimension one.

Original language	English
Pages (from-to)	1477–1497
Journal	Annali di Matematica Pura ed Applicata
Volume	197
Issue number	5
DOIs	https://doi.org/10.1007/s10231-018-0733-0
Publication status	Published - Oct 2018
MoE publication type	A1 Journal article-refereed

Keywords

Doubly nonlinear equation
Forward-in-time
Heat equation
Maximal operator
One-sided
p-Laplace
Parabolic BMO
Parabolic equation

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10.1007/s10231-018-0733-0

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AB - We study if the parabolic forward-in-time maximal operator is bounded on parabolic (Formula presented.). It turns out that for non-negative functions the answer is positive, but the behavior of sign-changing functions is more delicate. The class parabolic (Formula presented.) and the forward-in-time maximal operator originate from the regularity theory of nonlinear parabolic partial differential equations. In addition to that context, we also study the question in dimension one.

KW - Doubly nonlinear equation

KW - Forward-in-time

KW - Heat equation

KW - Maximal operator

KW - One-sided

KW - p-Laplace

KW - Parabolic BMO

KW - Parabolic equation

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Parabolic BMO and the forward-in-time maximal operator

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Keywords

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