Hilbert transform and related topics associated with the differential Jacobi operator on (0,+∞)

Hilbert transform and related topics associated with the differential Jacobi operator on (0,+∞) We define Hilbert transform and conjugate Poisson integrals associated with the Jacobi differential operator on (0, +∞). We prove that these operators are bounded in the appropriate Lebesgue spaces L p , 1 < p < +∞. In this study, the tools used are the Littlewood–Paley g-functions associated with the Poisson semigroup and the supplementary Poisson semigroup which we introduce in this paper. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Hilbert transform and related topics associated with the differential Jacobi operator on (0,+∞)

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Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2010 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0061-0
Publisher site
See Article on Publisher Site

Abstract

We define Hilbert transform and conjugate Poisson integrals associated with the Jacobi differential operator on (0, +∞). We prove that these operators are bounded in the appropriate Lebesgue spaces L p , 1 < p < +∞. In this study, the tools used are the Littlewood–Paley g-functions associated with the Poisson semigroup and the supplementary Poisson semigroup which we introduce in this paper.

Journal

PositivitySpringer Journals

Published: May 7, 2010

References

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