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MIXED NORM ESTIMATES FOR THE CESARO MEANS ASSOCIATED WITH DUNKL-HERMITE EXPANSIONS

Boggarapu, Pradeep and Roncal, Luz and Thangavelu, Sundaram (2017) MIXED NORM ESTIMATES FOR THE CESARO MEANS ASSOCIATED WITH DUNKL-HERMITE EXPANSIONS. In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369 (10). pp. 7021-7047.

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Official URL: http://doi.org/10.1090/tran/6861

Abstract

Our main goal in this article is to study mixed norm estimates for the Cesaro means associated with Dunkl-Hermite expansions on R-d. These expansions arise when one considers the Dunkl-Hermite operator (or Dunkl harmonic oscillator) H-kappa := -Delta(kappa)+vertical bar x vertical bar(2), where Delta(kappa)stands for the Dunkl-Laplacian. It is shown that the desired mixed norm estimates are equivalent to vector-valued inequalities for a sequence of Cesaro means for Laguerre expansions with shifted parameter. In order to obtain such vector-valued inequalities, we develop an argument to extend these Laguerre operators for complex values of the parameters involved and apply a version of the three lines lemma.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER MATHEMATICAL SOC, 201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 23 Sep 2017 05:08
Last Modified: 23 Sep 2017 05:08
URI: http://eprints.iisc.ac.in/id/eprint/57856

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