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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Dirichlet forms associated with hypercontractive semigroups


Author: James G. Hooton
Journal: Trans. Amer. Math. Soc. 253 (1979), 237-256
MSC: Primary 47D05; Secondary 47B25, 47F05
MathSciNet review: 536945
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Abstract: We exhibit a class of probability measures on $ {\textbf{R}^n}$ such that the associated Dirichlet form is represented by a selfadjoint operator A and such that $ {e^{ - tA}}$ is a hypercontractive semigroup of operators. The measures are of the form $ d\mu \, = \,{\Omega ^2}\,dx$ where $ \Omega $ has classical first derivatives and $ {L^p}$ second derivatives, p determined by n.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0536945-5
PII: S 0002-9947(1979)0536945-5
Keywords: Dirichlet form, hypercontractive semigroup, logarithmic Sobolev inequality, $ {L^p}$-contractive semigroup
Article copyright: © Copyright 1979 American Mathematical Society