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The sharp constant in the reverse Hölder inequality for Muckenhoupt weights. / Vasyunin, V.

In: St. Petersburg Mathematical Journal, Vol. 15, No. 1, 01.01.2004, p. 49-79.

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

Harvard

Vasyunin, V 2004, 'The sharp constant in the reverse Hölder inequality for Muckenhoupt weights', St. Petersburg Mathematical Journal, vol. 15, no. 1, pp. 49-79. https://doi.org/10.1090/S1061-0022-03-00802-1

APA

Vasyunin, V. (2004). The sharp constant in the reverse Hölder inequality for Muckenhoupt weights. St. Petersburg Mathematical Journal, 15(1), 49-79. https://doi.org/10.1090/S1061-0022-03-00802-1

Vancouver

Vasyunin V. The sharp constant in the reverse Hölder inequality for Muckenhoupt weights. St. Petersburg Mathematical Journal. 2004 Jan 1;15(1):49-79. https://doi.org/10.1090/S1061-0022-03-00802-1

Author

Vasyunin, V. / The sharp constant in the reverse Hölder inequality for Muckenhoupt weights. In: St. Petersburg Mathematical Journal. 2004 ; Vol. 15, No. 1. pp. 49-79.

BibTeX

@article{ebcd31d23abf406a85a586d595a383f5,
title = "The sharp constant in the reverse H{\"o}lder inequality for Muckenhoupt weights",
abstract = "Coifman and Fefferman proved that the “reverse H{\"o}lder inequality” is fulfilled for any weight satisfying the Muckenhoupt condition. In order to illustrate the power of the Bellman function technique, Nazarov, Volberg, and Treil showed (among other things) how this technique leads to the reverse H{\"o}lder inequality for the weights satisfying the dyadic Muckenhoupt condition on the real line. In this paper the proof of the reverse H{\"o}lder inequality with sharp constants is presented for the weights satisfying the usual (rather than dyadic) Muckenhoupt condition on the line. The results are a consequence of the calculation of the true Bellman function for the corresponding extremal problem.",
keywords = "Bellman function, Muckenhoupt weights, Reverse H{\"o}lder inequality",
author = "V. Vasyunin",
year = "2004",
month = jan,
day = "1",
doi = "10.1090/S1061-0022-03-00802-1",
language = "English",
volume = "15",
pages = "49--79",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "1",

}

RIS

TY - JOUR

T1 - The sharp constant in the reverse Hölder inequality for Muckenhoupt weights

AU - Vasyunin, V.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - Coifman and Fefferman proved that the “reverse Hölder inequality” is fulfilled for any weight satisfying the Muckenhoupt condition. In order to illustrate the power of the Bellman function technique, Nazarov, Volberg, and Treil showed (among other things) how this technique leads to the reverse Hölder inequality for the weights satisfying the dyadic Muckenhoupt condition on the real line. In this paper the proof of the reverse Hölder inequality with sharp constants is presented for the weights satisfying the usual (rather than dyadic) Muckenhoupt condition on the line. The results are a consequence of the calculation of the true Bellman function for the corresponding extremal problem.

AB - Coifman and Fefferman proved that the “reverse Hölder inequality” is fulfilled for any weight satisfying the Muckenhoupt condition. In order to illustrate the power of the Bellman function technique, Nazarov, Volberg, and Treil showed (among other things) how this technique leads to the reverse Hölder inequality for the weights satisfying the dyadic Muckenhoupt condition on the real line. In this paper the proof of the reverse Hölder inequality with sharp constants is presented for the weights satisfying the usual (rather than dyadic) Muckenhoupt condition on the line. The results are a consequence of the calculation of the true Bellman function for the corresponding extremal problem.

KW - Bellman function

KW - Muckenhoupt weights

KW - Reverse Hölder inequality

UR - http://www.scopus.com/inward/record.url?scp=34547609303&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-03-00802-1

DO - 10.1090/S1061-0022-03-00802-1

M3 - Article

AN - SCOPUS:34547609303

VL - 15

SP - 49

EP - 79

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 1

ER -

ID: 49879992