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Pointwise and norm estimates for operators associated with the Ornstein-Uhlenbeck semigroup by Trinidad Menárguez; Sonsoles Pérez; Fernando Soria is a Mathematics article available to read on EtoBox.

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## R&urn& In this Note, we find the explicit expression for the pointwise supremum of the kernels defining the Ornstein-Uhlenbeck semigroup. This allows us to give a more geometric proof of the weak type 1 for the Maximal Mehler transform, given in [7]. In addition, direct proofs of several results about the boundedness of the Riesz transforms of any order and the Littlewood-Paley ~1 function associated to this problem are presented. Estimntions ponctuelles et en norme pour des op&-uteurs associbs uu semi-groupe d'ornstein-Uhlenbeck Dans cette Note nous trvuvons 1 'expression explicite pour le supremum ponctuel des noyaux yui d+nis.sent le semi-groupe d'Ornstein~Uhlenbeck. Crci nous permet de dormer une d4mnn.rtrution plus g&me'triyur du ty>e ,filible 1 pour la tran~f&wation maximale dr Mehler, dorm&e dans [7]. De plus, nou.s prc'sentotw des d~morzstrcltions directes de plusieurs r&dtats cowernant lcs estimations pour les transfiwmations de Ries,: d'ordre quelconque et lu ji,nction g de Littlewood-Pale?; associe'e au probl>nre.

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Author

Trinidad Menárguez; Sonsoles Pérez; Fernando Soria

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0764-4442)

Published

1998

Language

EN

Field

Mathematics (Physical Sciences)