$B^q$ for parabolic measures

Sweezy, Caroline

B^{q}

for parabolic measures

Sweezy, Caroline

Studia Mathematica, Tome 129 (1998), p. 115-135 / Harvested from The Polish Digital Mathematics Library

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Résumé

If Ω is a Lip(1,1/2) domain, μ a doubling measure on $\partial_{p} Ω, \partial / \partial t - L_{i}$ , 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 $ω_{0} \in B^{q} (μ)$ 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 $ω_{0} \in B^{q} (μ)$ implies $ω_{1} \in B^{q} (μ)$ 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.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:216568

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     author = {Caroline Sweezy},
     title = {$B^q$ for parabolic measures},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {115-135},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p115bwm}
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Sweezy, Caroline. $B^q$ for parabolic measures. Studia Mathematica, Tome 129 (1998) pp. 115-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p115bwm/

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