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Maximal operators of Fejér means of double Vilenkin-Fourier series

István Blahota, György Gát, Ushangi Goginava (2007)

Colloquium Mathematicae

The main aim of this paper is to prove that the maximal operator σ * : = s u p | σ n , n | of the Fejér means of the double Vilenkin-Fourier series is not bounded from the Hardy space H 1 / 2 to the space weak- L 1 / 2 .

Measures and lacunary sets

Pascal Lefèvre (1999)

Studia Mathematica

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.

Mesures spectrales de Walsh associées à certaines suites arithmétiques

Jean Coquet (1985)

Annales de l'institut Fourier

On associe à certaines suites g de nombres complexes une mesure borélienne positive μ g sur le tore dont la transformée de Fourier-Walsh est une suite de moyennes liées à g . La nature de μ g (discrète, continue) est discutée dans quelques cas : suites presque-périodiques et certaines suites arithmétiques.

Multipliers for Hermite expansions.

Sundaram Thangavelu (1987)

Revista Matemática Iberoamericana

The aim of this paper is to prove certain multiplier theorems for the Hermite series.

Multipliers of Laplace transform type for Laguerre and Hermite expansions

Pablo L. De Nápoli, Irene Drelichman, Ricardo G. Durán (2011)

Studia Mathematica

We present a new criterion for the weighted L p - L q 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

Błażej Wróbel (2013)

Studia Mathematica

Multivariate spectral multipliers for systems of Ornstein-Uhlenbeck operators are studied. We prove that L p -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.

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