Extremizers and sharp weak-type estimates for positive dyadic shifts

Guillermo Rey; Alexander Reznikov

doi:10.1016/j.aim.2013.12.030

Extremizers and sharp weak-type estimates for positive dyadic shifts

Guillermo Rey, Alexander Reznikov

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

9 Scopus citations

Abstract

We find the exact Bellman function for the weak ^L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.

Original language	English (US)
Pages (from-to)	664-681
Number of pages	18
Journal	Advances in Mathematics
Volume	254
DOIs	https://doi.org/10.1016/j.aim.2013.12.030
State	Published - Mar 20 2014
Externally published	Yes

Keywords

Bellman functions
Dyadic shifts
Sharp weak-type estimates

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10.1016/j.aim.2013.12.030

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title = "Extremizers and sharp weak-type estimates for positive dyadic shifts",

abstract = "We find the exact Bellman function for the weak L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.",

keywords = "Bellman functions, Dyadic shifts, Sharp weak-type estimates",

author = "Guillermo Rey and Alexander Reznikov",

year = "2014",

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day = "20",

doi = "10.1016/j.aim.2013.12.030",

language = "English (US)",

volume = "254",

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journal = "Advances in Mathematics",

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TY - JOUR

T1 - Extremizers and sharp weak-type estimates for positive dyadic shifts

AU - Rey, Guillermo

AU - Reznikov, Alexander

PY - 2014/3/20

Y1 - 2014/3/20

N2 - We find the exact Bellman function for the weak L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.

AB - We find the exact Bellman function for the weak L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.

KW - Bellman functions

KW - Dyadic shifts

KW - Sharp weak-type estimates

UR - https://www.scopus.com/pages/publications/84892638381

UR - https://www.scopus.com/inward/citedby.url?scp=84892638381&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2013.12.030

DO - 10.1016/j.aim.2013.12.030

M3 - Article

AN - SCOPUS:84892638381

SN - 0001-8708

VL - 254

SP - 664

EP - 681

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Extremizers and sharp weak-type estimates for positive dyadic shifts

Abstract

Keywords

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