Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu, and Dachun Yang. "Weighted norm inequalities for maximal singular integrals with nondoubling measures." Studia Mathematica 187.2 (2008): 101-123. <http://eudml.org/doc/284902>.

@article{GuoenHu2008,
abstract = {Let μ be a nonnegative Radon measure on $ℝ^\{d\}$ which satisfies μ(B(x,r)) ≤ Crⁿ for any $x ∈ ℝ^\{d\}$ and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with $A_\{p\}^\{ϱ\}(μ)$ weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with $A_\{∞\}^\{ϱ\}(μ)$ weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).},
author = {Guoen Hu, Dachun Yang},
journal = {Studia Mathematica},
keywords = {nondoubling measure; singular integral; sharp maximal operator; weight},
language = {eng},
number = {2},
pages = {101-123},
title = {Weighted norm inequalities for maximal singular integrals with nondoubling measures},
url = {http://eudml.org/doc/284902},
volume = {187},
year = {2008},
}

TY - JOUR
AU - Guoen Hu
AU - Dachun Yang
TI - Weighted norm inequalities for maximal singular integrals with nondoubling measures
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 2
SP - 101
EP - 123
AB - Let μ be a nonnegative Radon measure on $ℝ^{d}$ which satisfies μ(B(x,r)) ≤ Crⁿ for any $x ∈ ℝ^{d}$ and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with $A_{p}^{ϱ}(μ)$ weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with $A_{∞}^{ϱ}(μ)$ weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
LA - eng
KW - nondoubling measure; singular integral; sharp maximal operator; weight
UR - http://eudml.org/doc/284902
ER -