Jean-Philippe Anker
Institut Denis Poisson, Université d’Orléans
https://www.idpoisson.fr/anker/
Date(s) : 10/03/2014 iCal
11 h 15 min - 12 h 15 min
Hardy space H1 within the framework of rational Dunkl theory
Rational Dunkl theory is a distortion of Euclidean Fourier analysis, which has developed over 25 years in connection with the theory of special functions related to root systems. In this talk we present a recent work [hal-00864457], in collaboration with Néjib Ben Salem (Tunis), Jacek Dziubanski (Wroclaw) and Nabila Hamda (Tunis), where we studied the Hardy H1 space within the framework of rational Dunkl’s theory. More precisely, in dimension 1, we obtained the equivalence between two definitions of the Hardy space H1, on the one hand the atomic definition and on the other hand the definition by means of the maximal function associated with the semi-group of the heat. On this occasion we observed that the heat core is not Gaussian. However, we have succeeded in establishing the equivalence between the two definitions by following the Uchiyama approach.
https://hal.archives-ouvertes.fr/hal-00864457/
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