Maximal operators related to the Ornstein-Uhlenbeck semigroup with complex time parameter
Journal article, 2006
Let γ be the Gaussian measure in Click to view the MathML source and Click to view the MathML source, t>0, the corresponding Ornstein-Uhlenbeck semigroup, whose infinitesimal generator is Click to view the MathML source. For each p with 12 this operator is of weak type but not of strong type (p,p) for γ. However, if a neighbourhood of the origin is deleted from Ep in the definition of Click to view the MathML source, the resulting operator is shown to be of strong type.
Gaussian measure
Ornstein-Uhlenbeck semigroup
Maximal operators
Mehler kernel
Author
Peter Sjögren
Chalmers, Mathematical Sciences
University of Gothenburg
Journal of Functional Analysis
0022-1236 (ISSN) 1096-0783 (eISSN)
Vol. 237 2 675-688Subject Categories
Mathematics
DOI
10.1016/j.jfa.2005.12.005