Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 34, 2009, 523-528

CAMPANATO THEOREM ON METRIC MEASURE SPACES

Przemyslaw Górka

Universidad de Talca, Instituto de Matemática y Física
Casilla 747, Talca, Chile

and

Warsaw University of Technology, Department of Mathematics and Information Sciences
Pl. Politechniki 1, 00-661 Warsaw, Poland; pgorka 'at' mini.pw.edu.pl

Abstract. We prove the Campanato theorem on a metric space. The theorem characterizes Hölder continuous functions by the growth of their local integrals. As a byproduct we obtain Morrey theorem on Hajlasz-Sobolev spaces.

2000 Mathematics Subject Classification: Primary 28C99, 46E35.

Key words: Metric measure space, doubling measure, Campanato theorem, Hölder continuous function.

Reference to this article: P. Górka: Campanato theorem on metric measure spaces. Ann. Acad. Sci. Fenn. Math. 34 (2009), 523-528.

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