Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem
Annales de l'Institut Fourier, Volume 38 (1988) no. 1, p. 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,kHZ 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,kZ est borné sur L p , 1<p<. Nous appliquons ce théorème pour obtenir une extension du théorème de multiplicateurs de Marcinkiewicz.

@article{AIF_1988__38_1_157_0,
     author = {Carbery, Anthony},
     title = {Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {38},
     number = {1},
     year = {1988},
     pages = {157-168},
     doi = {10.5802/aif.1127},
     zbl = {0607.42009},
     mrnumber = {89h:42026},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1988__38_1_157_0}
}
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. http://www.numdam.org/item/AIF_1988__38_1_157_0/

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