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2004 Superposition operators on Dirichlet spaces
Patrick J. Fitzsimmons
Tohoku Math. J. (2) 56(3): 327-340 (2004). DOI: 10.2748/tmj/1113246670

Abstract

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. The proofs rely on a co-area formula for condenser potentials.

Citation

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Patrick J. Fitzsimmons. "Superposition operators on Dirichlet spaces." Tohoku Math. J. (2) 56 (3) 327 - 340, 2004. https://doi.org/10.2748/tmj/1113246670

Information

Published: 2004
First available in Project Euclid: 11 April 2005

zbMATH: 1067.31010
MathSciNet: MR2075769
Digital Object Identifier: 10.2748/tmj/1113246670

Subjects:
Primary: 31C25
Secondary: 46E35, 46H30, 60J45

Rights: Copyright © 2004 Tohoku University

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Vol.56 • No. 3 • 2004
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