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Applications of weighted estimates of Calderon's commutators. / Merkulov, A. S.; Shirokov, N. A.

In: Vestnik St. Petersburg University: Mathematics, Vol. 45, No. 2, 01.04.2012, p. 93-97.

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

Harvard

Merkulov, AS & Shirokov, NA 2012, 'Applications of weighted estimates of Calderon's commutators', Vestnik St. Petersburg University: Mathematics, vol. 45, no. 2, pp. 93-97. https://doi.org/10.3103/S1063454112020094

APA

Merkulov, A. S., & Shirokov, N. A. (2012). Applications of weighted estimates of Calderon's commutators. Vestnik St. Petersburg University: Mathematics, 45(2), 93-97. https://doi.org/10.3103/S1063454112020094

Vancouver

Merkulov AS, Shirokov NA. Applications of weighted estimates of Calderon's commutators. Vestnik St. Petersburg University: Mathematics. 2012 Apr 1;45(2):93-97. https://doi.org/10.3103/S1063454112020094

Author

Merkulov, A. S. ; Shirokov, N. A. / Applications of weighted estimates of Calderon's commutators. In: Vestnik St. Petersburg University: Mathematics. 2012 ; Vol. 45, No. 2. pp. 93-97.

BibTeX

@article{555178452c764e98bb0df13f04cd2c7d,
title = "Applications of weighted estimates of Calderon's commutators",
abstract = "The paper introduces singular integral operators of a new type defined in the space L p with the weight function on the complex plane. For these operators, norm estimates are derived. Namely, if V is a complex-valued function on the complex plane satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe} and F is an entire function, then we put, It is shown that if the weight function ω is a Muckenhoupt A p weight for 1 < p < ∞, then {pipe}{pipe}P * Ff{pipe}{pipe} p, ω ≤ C(F, w, p){pipe}{pipe}f{pipe}{pipe} p, ω.",
keywords = "Calderon's commutators, Muckenhoupt weights, singular integrals",
author = "Merkulov, {A. S.} and Shirokov, {N. A.}",
year = "2012",
month = apr,
day = "1",
doi = "10.3103/S1063454112020094",
language = "English",
volume = "45",
pages = "93--97",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Applications of weighted estimates of Calderon's commutators

AU - Merkulov, A. S.

AU - Shirokov, N. A.

PY - 2012/4/1

Y1 - 2012/4/1

N2 - The paper introduces singular integral operators of a new type defined in the space L p with the weight function on the complex plane. For these operators, norm estimates are derived. Namely, if V is a complex-valued function on the complex plane satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe} and F is an entire function, then we put, It is shown that if the weight function ω is a Muckenhoupt A p weight for 1 < p < ∞, then {pipe}{pipe}P * Ff{pipe}{pipe} p, ω ≤ C(F, w, p){pipe}{pipe}f{pipe}{pipe} p, ω.

AB - The paper introduces singular integral operators of a new type defined in the space L p with the weight function on the complex plane. For these operators, norm estimates are derived. Namely, if V is a complex-valued function on the complex plane satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe} and F is an entire function, then we put, It is shown that if the weight function ω is a Muckenhoupt A p weight for 1 < p < ∞, then {pipe}{pipe}P * Ff{pipe}{pipe} p, ω ≤ C(F, w, p){pipe}{pipe}f{pipe}{pipe} p, ω.

KW - Calderon's commutators

KW - Muckenhoupt weights

KW - singular integrals

UR - http://www.scopus.com/inward/record.url?scp=84870311458&partnerID=8YFLogxK

U2 - 10.3103/S1063454112020094

DO - 10.3103/S1063454112020094

M3 - Article

AN - SCOPUS:84870311458

VL - 45

SP - 93

EP - 97

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 48397446