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Sharp estimates for the Ornstein-Uhlenbeck operator

Giancarlo Mauceri, Stefano Meda, Peter Sjögren (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure γ on d . We prove a sharp estimate of the operator norm of the imaginary powers of on L p ( γ ) , 1 < p < ...

Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications

José María Martell (2004)

Studia Mathematica

In the context of the spaces of homogeneous type, given a family of operators that look like approximations of the identity, new sharp maximal functions are considered. We prove a good-λ inequality for Muckenhoupt weights, which leads to an analog of the Fefferman-Stein estimate for the classical sharp maximal function. As a consequence, we establish weighted norm estimates for certain singular integrals, defined on irregular domains, with Hörmander conditions replaced by some estimates which do...

Shift invariant measures and simple spectrum

A. Kłopotowski, M. Nadkarni (2000)

Colloquium Mathematicae

We consider some descriptive properties of supports of shift invariant measures on under the assumption that the closed linear span (in L 2 ) of the co-ordinate functions on is all of L 2 .

Simultaneous solutions of operator Sylvester equations

Sang-Gu Lee, Quoc-Phong Vu (2014)

Studia Mathematica

We consider simultaneous solutions of operator Sylvester equations A i X - X B i = C i (1 ≤ i ≤ k), where ( A , . . . , A k ) and ( B , . . . , B k ) are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and ( C , . . . , C k ) is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of ( A , . . . , A k ) and ( B , . . . , B k ) do not intersect, then this system of Sylvester equations has a unique simultaneous solution.

Single valued extension property and generalized Weyl’s theorem

M. Berkani, N. Castro, S. V. Djordjević (2006)

Mathematica Bohemica

Let T be an operator acting on a Banach space X , let σ ( T ) and σ B W ( T ) be respectively the spectrum and the B-Weyl spectrum of T . We say that T satisfies the generalized Weyl’s theorem if σ B W ( T ) = σ ( T ) E ( T ) , where E ( T ) is the set of all isolated eigenvalues of T . The first goal of this paper is to show that if T is an operator of topological uniform descent and 0 is an accumulation point of the point spectrum of T , then T does not have the single valued extension property at 0 , extending an earlier result of J. K. Finch and a...

Ski de fond

Alain Dufresnoy (1983/1984)

Séminaire de théorie spectrale et géométrie

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