ISSN:
1572-929X
Keywords:
Calderón–Zygmund operators
;
Gaussian measure
;
Hermite polynomials
;
Mehler kernel
;
Ornstein–Uhlenbeck semigroup
;
Riesz transforms.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We prove that the second-order Riesz transforms associated to the Ornstein–Uhlenbeck semigroup are weak type (1,1) with respect to the Gaussian measure in finite dimension. We also show that they are given by a principal value integral plus a constant multiple of the identity. For the Riesz transforms of order three or higher, we present a counterexample showing that the weak type (1,1) estimate fails.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008685801945
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