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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## $B^q$ for parabolic measures

### Tom 131 / 1998

Studia Mathematica 131 (1998), 115-135 DOI: 10.4064/sm-131-2-115-135

#### Streszczenie

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.

#### Autorzy

• Caroline Sweezy

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