We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
On associe à certaines suites de nombres complexes une mesure borélienne positive sur le tore dont la transformée de Fourier-Walsh est une suite de moyennes liées à . La nature de (discrète, continue) est discutée dans quelques cas : suites presque-périodiques et certaines suites arithmétiques.
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.
We show that in for p ≠ 2 the constants of equivalence between finite initial segments of the Walsh and trigonometric systems have power type growth. We also show that the Riemann ideal norms connected with those systems have power type growth.
The main aim of this paper is to prove that there exists a martingale such that the Fejér means of the two-dimensional Walsh-Fourier series of f is not uniformly bounded in the space weak-.