TY - JOUR

T1 - Weighted estimates of Calderon's commutators on complex plane

AU - Merkulov, A. S.

AU - Shirokov, N. A.

PY - 2010/9/1

Y1 - 2010/9/1

N2 - Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe}, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A p weight on ℂ; i. e., the inequality, holds for any disk B, {pipe}B{pipe} = σ(B), and σ be the Lebesque measure on ℂ. We define the operator T* n as follows: The main result of this work consists in deriving the estimate, where b(p, n) grows as a power of n.

AB - Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe}, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A p weight on ℂ; i. e., the inequality, holds for any disk B, {pipe}B{pipe} = σ(B), and σ be the Lebesque measure on ℂ. We define the operator T* n as follows: The main result of this work consists in deriving the estimate, where b(p, n) grows as a power of n.

KW - Calderon's commutators

KW - Muckenhoupt weights

KW - singular integrals

UR - http://www.scopus.com/inward/record.url?scp=84859726404&partnerID=8YFLogxK

U2 - 10.3103/S1063454110030064

DO - 10.3103/S1063454110030064

M3 - Article

AN - SCOPUS:84859726404

VL - 43

SP - 163

EP - 168

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -