Monge-Ampère equations and Bellman functions: The dyadic maximal operator

Leonid Slavin; Alexander Stokolos; Vasily Vasyunin

doi:10.1016/j.crma.2008.03.003

Monge-Ampère equations and Bellman functions: The dyadic maximal operator

Leonid Slavin
, Alexander Stokolos
, Vasily Vasyunin

Mathematical Sciences

University of Missouri
DePaul University
RAS - Saint Petersburg Department of Steklov Institute of Mathematics

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

49 Scopus citations

Abstract

We find explicitly the Bellman function for the dyadic maximal operator on L^p as the solution of a Bellman partial differential equation of Monge-Ampère type. This function has been previously found by A. Melas (2005) in a different way, but it is our partial differential equation-based approach that is of principal interest here. Clear and replicable, it holds promise as a unifying template for past and current Bellman function investigations. To cite this article: L. Slavin et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

Original language	English
Pages (from-to)	585-588
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	346
Issue number	9-10
DOIs	https://doi.org/10.1016/j.crma.2008.03.003
State	Published - May 2008

Scopus Subject Areas

General Mathematics

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10.1016/j.crma.2008.03.003

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title = "Monge-Amp{\`e}re equations and Bellman functions: The dyadic maximal operator",

abstract = "We find explicitly the Bellman function for the dyadic maximal operator on Lp as the solution of a Bellman partial differential equation of Monge-Amp{\`e}re type. This function has been previously found by A. Melas (2005) in a different way, but it is our partial differential equation-based approach that is of principal interest here. Clear and replicable, it holds promise as a unifying template for past and current Bellman function investigations. To cite this article: L. Slavin et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).",

author = "Leonid Slavin and Alexander Stokolos and Vasily Vasyunin",

year = "2008",

month = may,

doi = "10.1016/j.crma.2008.03.003",

language = "English",

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TY - JOUR

T1 - Monge-Ampère equations and Bellman functions

T2 - The dyadic maximal operator

AU - Slavin, Leonid

AU - Stokolos, Alexander

AU - Vasyunin, Vasily

PY - 2008/5

Y1 - 2008/5

N2 - We find explicitly the Bellman function for the dyadic maximal operator on Lp as the solution of a Bellman partial differential equation of Monge-Ampère type. This function has been previously found by A. Melas (2005) in a different way, but it is our partial differential equation-based approach that is of principal interest here. Clear and replicable, it holds promise as a unifying template for past and current Bellman function investigations. To cite this article: L. Slavin et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

AB - We find explicitly the Bellman function for the dyadic maximal operator on Lp as the solution of a Bellman partial differential equation of Monge-Ampère type. This function has been previously found by A. Melas (2005) in a different way, but it is our partial differential equation-based approach that is of principal interest here. Clear and replicable, it holds promise as a unifying template for past and current Bellman function investigations. To cite this article: L. Slavin et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

UR - https://www.scopus.com/pages/publications/42649083996

U2 - 10.1016/j.crma.2008.03.003

DO - 10.1016/j.crma.2008.03.003

M3 - Article

SN - 1631-073X

VL - 346

SP - 585

EP - 588

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9-10

ER -

Monge-Ampère equations and Bellman functions: The dyadic maximal operator

Abstract

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