Superposition operators on Dirichlet spaces
Fitzsimmons, Patrick J.
Tohoku Math. J. (2), Tome 56 (2004) no. 1, p. 327-340 / Harvested from Project Euclid
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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.
Publié le : 2004-09-14
Classification:  31C25,  46E35,  46H30,  60J45 
@article{1113246670,
     author = {Fitzsimmons, Patrick J.},
     title = {Superposition operators on Dirichlet spaces},
     journal = {Tohoku Math. J. (2)},
     volume = {56},
     number = {1},
     year = {2004},
     pages = { 327-340},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1113246670}
}

Fitzsimmons, Patrick J. Superposition operators on Dirichlet spaces. Tohoku Math. J. (2), Tome 56 (2004) no. 1, pp.  327-340. http://gdmltest.u-ga.fr/item/1113246670/