Research ArticleOpen accessPhrase in the titleIntroduction to the Besov Spaces and Triebel-Lizorkin Spaces for Hermite and Laguerre expansions and some applicationsA. Iris, P. LopezWe introduced new definitions of Besov spaces and Triebel-Lizorkin spaces associated with multidimensional Hermite expansions and multidimensional Laguerre expansions. We showed that the set of p-integrable functions is a Triebel-Lizorkin space with respect to the Gaussian measure and similarly, with respect to the probabilistic Gamma measure. Also, we showed that the Gaussian Sobolev spaces and Laguerre Sobolev spaces are Triebel-Lizorkin … …Journal of Mathematics and Statistics, Vol. 1, Issue 3 · 30 Sep 2005 · 7,580 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleLimit Theorems for a Class of Additive Functionals of Symmetric Stable Process and Fractional Brownian Motion in Besov-Orlicz SpacesM. Ait Ouahra, A. Kissami, A. SghirWe use the Potter's Theorem and the tightness criterion in Besov-Orlicz spaces, recently proved, to generalize some limit theorem for occupation times problem of certain self-similar process, namely symmetric stable process of index 1<α≤ and fractional Brownian motion of Hurst parameter 0<H<1. We give also strong approximation version of our limit theorem, more precisely, we show Lp-estimate version. …Journal of Mathematics and Statistics, Vol. 8, Issue 4 · 22 Feb 2013 · 6,757 accessesView PDFCite