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A weighted Poincaré inequality with a doubling weight

Author(s): Ritva Hurri-Syrjanen
Journal: Proc. Amer. Math. Soc. 126 (1998), 545-552.
MSC (1991): Primary 46Exx, 26Dxx
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Abstract: We show that unbounded John domains (and even a larger class of domains than John domains) satisfy the weighted Poincaré inequality

\begin{equation*}\inf _{a\in \mathbb{R}} \|u(x)-a\|_{L^{q}(D,w_{1})} \le C\|\nabla u(x)\|_{L^{p}(D,w_{2})}\end{equation*}

whenever $u$ is a Lipschitz function on $D$, $w_{1}$ is a doubling weight, and weights satisfy certain cube conditions, and $C=C(D,p,q,w_{1},w_{2})$.

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Additional Information:

Ritva Hurri-Syrjanen
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Address at time of publication: Department of Mathematics, P.O. Box 4, FIN-00014 University of Helsinki, Finland
Email: syrjanen@math.utexas.edu, hurrisyr@helsinki.fi

DOI: 10.1090/S0002-9939-98-04059-3
PII: S 0002-9939(98)04059-3
Received by editor(s): January 5, 1996
Received by editor(s) in revised form: August 22, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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