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

Studia Mathematica (1998)

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

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topSweezy, 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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