We show that the maximal operator associated to the family of rectangles in one of whose sides is parallel to for some j,k is bounded on , . 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 dont un des côtés est parallèle à pour quelques est borné sur , . 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}, pages = {157--168}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {1}, year = {1988}, doi = {10.5802/aif.1127}, mrnumber = {89h:42026}, zbl = {0607.42009}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1127/} }
TY - JOUR AU - Carbery, Anthony TI - Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem JO - Annales de l'Institut Fourier PY - 1988 SP - 157 EP - 168 VL - 38 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1127/ DO - 10.5802/aif.1127 LA - en ID - AIF_1988__38_1_157_0 ER -
%0 Journal Article %A Carbery, Anthony %T Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem %J Annales de l'Institut Fourier %D 1988 %P 157-168 %V 38 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1127/ %R 10.5802/aif.1127 %G en %F 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/articles/10.5802/aif.1127/
[1] An almost-orthogonality principle with applications to maximal functions associated to convex bodies, B.A.M.S., 14-2 (1986), 269-273. | MR | Zbl
. —[2] Variants of the Calderón-Zygmund theory for Lp-spaces, Revista Matemática Ibero Americana, 2-4 (1986), 381-396. | MR | Zbl
. —[3] Personal communication.
. —[4] Maximal operators related to the Radon transform and the Calderón-Zygmund method of rotations, Duke Math. J., 53-1 (1986), 189-209. | MR | Zbl
, AND .[5] Differentiation in lacunary directions, P.N.A.S. (USA), 75-3 (1978), 1060-1062. | MR | Zbl
, AND . —[6] Singular integrals and differentiability properties of functions, Princeton University Press, Princeton N.J., 1970. | MR | Zbl
. —Cited by Sources: