no. 1
Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
Annales de l'Institut Fourier, Volume 38 (1988) no. 1, pp. 157-168

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∈HZ is bounded on L p , 1<p<∞. We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.

Nous montrons que l’opérateur maximal associé à la famille de rectangles en R 3 dont un des côtés est parallèle à (1,2 j ,2 k ) pour quelques j,k∈Z est borné sur L p , 1<p<∞. Nous appliquons ce théorème pour obtenir une extension du théorème de multiplicateurs de Marcinkiewicz.

Carbery, Anthony. Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem. Annales de l'Institut Fourier, Volume 38 (1988) no. 1, pp. 157-168. doi: 10.5802/aif.1127
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