En utilisant le théorème de Ruelle d'opérateur de transfert, nous démontrons que la moyenne 2-k Σn=02k-1 ||^wn||L1 de la localisation fréquentielle pour les paquets d'ondelettes admet un équivalent de la forme cρk (c > 0, 1 < ρ < √2). Cela améliore une inégalité antérieurement obtenue par Coifman, Meyer et Wickerhauser. Des estimations numériques de ρ sont obtenues pour des filtres de Daubechies.
We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.
The aim of this paper is to prove certain multiplier theorems for the Hermite series.
We study boundedness of certain multiplier transforms associated to the special Hermite operator.
We present a new criterion for the weighted boundedness of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we recover known results on weighted estimates for Laguerre and Hermite fractional integrals with a unified and simpler approach.
Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators are studied. We prove that -uniform, 1 < p < ∞, spectral multipliers extend to holomorphic functions in some subset of a polysector, depending on p. We also characterize L¹-uniform spectral multipliers and prove a Marcinkiewicz-type multiplier theorem. In the appendix we obtain analogous results for systems of Laguerre operators.