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- Title
Hilbert, Dirichlet and Fejér families of operators arising from C<sub>0</sub>-groups, cosine functions and holomorphic semigroups.
- Authors
Fašangová, Eva; Miana, Pedro J.
- Abstract
The main aim of this paper is to extend definitions of Hilbert transform, Dirichlet and Fejér operators (defined by convolution with suitable kernels in Lebesgue spaces) in arbitrary Banach spaces. We present a self-contained theory which includes different approaches of other authors whose starting points were usually C0-groups or cosine functions. We present relations with holomorphic semigroups. We characterize the geometric property of UMD spaces in terms of the Dirichlet and Fejér operators. To end the paper, we give examples to illustrate our results.
- Subjects
SEMIGROUPS (Algebra); SEMIGROUPS of operators; HILBERT transform; DIRICHLET forms; HOLOMORPHIC functions; MATHEMATICAL functions
- Publication
Semigroup Forum, 2010, Vol 80, Issue 1, p33
- ISSN
0037-1912
- Publication type
Article
- DOI
10.1007/s00233-009-9181-x