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We show that the maximal operator associated to the family of rectangles in $R^{3}$ one of whose sides is parallel to $(1, 2^{j}, 2^{k})$ for some j,k $\in H Z$ is bounded on $L^{p}$ , $1 < p < \infty$ . We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.

Disjointness results for some classes of stable processes

Michael Hernández, Christian Houdré (1993)

Studia Mathematica

We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.

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Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé I : les inégalités classiques

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé II : l'opérateur carré du champ

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé IV : semi-groupes de convolution symétriques

Démonstration probabiliste de certaines inégalités de Littlewood-Paley. Exposé III : les inégalités générales

Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem

Disjointness results for some classes of stable processes

Currently displaying 1 – 6 of 6