Proceedings ArticleDOI
A weak 2-weight problem for the Poisson-Hermite semigroup
Gustavo Garrigós
- pp 153-171
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Abstract:
This survey is a slightly extended version of the lecture given by the author at the VI International Course of Mathematical Analysis in Andalućıa (CIDAMA), in September 2014. Most results form part of the paper [3], written jointly with S. Hartzstein, T. Signes, J.L. Torrea and B. Viviani.read more
Citations
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Journal ArticleDOI
Special Functions and Their Applications. By N. N. Lebedev, translated by R. A. Silverman. Pp. xii, 308. 96s. 1965. (Prentice-Hall)
Journal ArticleDOI
A.e. convergence and 2-weight inequalities for Poisson-Laguerre semigroups
TL;DR: In this paper, the Poisson kernels associated with various Laguerre-type operators were analyzed and the optimal decay estimates for the poisson kernels were derived. But the decay estimates were not obtained for the Poison kernels associated to the Laguera-type operator.
Pointwise convergence of fractional powers of Hermite type operators
TL;DR: In this article , minimal integrability and smoothness conditions on a function f were obtained for the Hermite or Ornstein-Uhlenbeck operator, where f is a function and f is well-defined at a given point.
References
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Book
Topics in Harmonic Analysis Related to the Littlewood-Paley Theory.
TL;DR: In this article, an extension of the classical Littlewood-Paley theory in the context of symmetric diffusion semigroups is presented. But this work is restricted to the case of second order elliptic operators.
Journal ArticleDOI
Special Functions and Their Applications. By N. N. Lebedev, translated by R. A. Silverman. Pp. xii, 308. 96s. 1965. (Prentice-Hall)
Book
Lectures on Hermite and Laguerre expansions
TL;DR: The main thrust of as discussed by the authors is to develop a concrete Littlewood-Paley-Stein theory for these expansions and use the theory to prove multiplier theorems, and most of the results in this monograph appear for the first time in book form.
Journal ArticleDOI
Extension Problem and Harnack's Inequality for Some Fractional Operators
Pablo Raúl Stinga,José L. Torrea +1 more
TL;DR: In this article, the fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space of the harmonic oscillator.