Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 38, 2013, 721-726

ON WEIGHTED POINCARÉ INEQUALITIES

Bartlomiej Dyda and Moritz Kassmann

Wroclaw University of Technology, Institute of Mathematics and Computer Science
Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland; bdyda 'at' pwr.wroc.pl
and Universität Bielefeld, Fakultät für Mathematik
Postfach 100131, D-33501 Bielefeld, Germany; dyda@math.uni-bielefeld.de

Universität Bielefeld, Fakultät für Mathematik
Postfach 100131, D-33501 Bielefeld, Germany; moritz.kassmann 'at' uni-bielefeld.de

Abstract. The aim of this note is to show that Poincaré inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincaré inequalities are considered, too. The proof is short and does not involve covering arguments.

2010 Mathematics Subject Classification: Primary 35A23; Secondary 26D10, 26D15.

Key words: Dirichlet forms, Sobolev spaces, Poincaré inequality, fractional Poincaré inequality.

Reference to this article: B. Dyda and M. Kassmann: On weighted Poincaré inequalities. Ann. Acad. Sci. Fenn. Math. 38 (2013), 721-726.

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doi:10.5186/aasfm.2013.3834