# ${B}^{q}$ for parabolic measures

Studia Mathematica (1998)

• Volume: 131, Issue: 2, page 115-135
• ISSN: 0039-3223

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## Abstract

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If Ω is a Lip(1,1/2) domain, μ a doubling measure on ${\partial }_{p}\Omega ,\partial /\partial t-{L}_{i}$, i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures ${\omega }_{0}$, ${\omega }_{1}$ have the property that ${\omega }_{0}\in {B}^{q}\left(\mu \right)$ implies ${\omega }_{1}$ is absolutely continuous with respect to ${\omega }_{0}$ whenever a certain Carleson-type condition holds on the difference function of the coefficients of ${L}_{1}$ and ${L}_{0}$. Also ${\omega }_{0}\in {B}^{q}\left(\mu \right)$ implies ${\omega }_{1}\in {B}^{q}\left(\mu \right)$ whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures extended to parabolic-type measures on time-varying domains. The method of proof is that of Fefferman, Kenig and Pipher.

## How to cite

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Sweezy, Caroline. "$B^q$ for parabolic measures." Studia Mathematica 131.2 (1998): 115-135. <http://eudml.org/doc/216568>.

@article{Sweezy1998,
abstract = {If Ω is a Lip(1,1/2) domain, μ a doubling measure on $∂_\{p\}Ω, ∂/∂t - L_\{i\}$, i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures $ω_\{0\}$, $ω_\{1\}$ have the property that $ω_\{0\} ∈ B^\{q\}(μ)$ implies $ω_\{1\}$ is absolutely continuous with respect to $ω_\{0\}$ whenever a certain Carleson-type condition holds on the difference function of the coefficients of $L_\{1\}$ and $L_\{0\}$. Also $ω_\{0\} ∈ B^\{q\}(μ)$ implies $ω_\{1\} ∈ B^\{q\}(μ)$ whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures extended to parabolic-type measures on time-varying domains. The method of proof is that of Fefferman, Kenig and Pipher.},
author = {Sweezy, Caroline},
journal = {Studia Mathematica},
keywords = {parabolic-type measures; Lip (1,1/2) domain; good-λ inequalities; coefficients bounded and measurable; Carleson-type condition; time-varying domains},
language = {eng},
number = {2},
pages = {115-135},
title = {$B^q$ for parabolic measures},
url = {http://eudml.org/doc/216568},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Sweezy, Caroline
TI - $B^q$ for parabolic measures
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 2
SP - 115
EP - 135
AB - If Ω is a Lip(1,1/2) domain, μ a doubling measure on $∂_{p}Ω, ∂/∂t - L_{i}$, i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures $ω_{0}$, $ω_{1}$ have the property that $ω_{0} ∈ B^{q}(μ)$ implies $ω_{1}$ is absolutely continuous with respect to $ω_{0}$ whenever a certain Carleson-type condition holds on the difference function of the coefficients of $L_{1}$ and $L_{0}$. Also $ω_{0} ∈ B^{q}(μ)$ implies $ω_{1} ∈ B^{q}(μ)$ whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures extended to parabolic-type measures on time-varying domains. The method of proof is that of Fefferman, Kenig and Pipher.
LA - eng
KW - parabolic-type measures; Lip (1,1/2) domain; good-λ inequalities; coefficients bounded and measurable; Carleson-type condition; time-varying domains
UR - http://eudml.org/doc/216568
ER -

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