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

Carbery, Anthony. "Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem." Annales de l'institut Fourier 38.1 (1988): 157-168. <http://eudml.org/doc/74787>.

@article{Carbery1988,
abstract = {We show that the maximal operator associated to the family of rectangles in $\{\bf R\}^ 3$ one of whose sides is parallel to $(1,2^ j,2^ k)$ for some j,k$\in \{\bf H\}Z$ is bounded on $L^ p$, $1&lt; p&lt; \infty $. We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.},
author = {Carbery, Anthony},
journal = {Annales de l'institut Fourier},
keywords = {maximal operator; Marcinkiewicz multiplier theorem},
language = {eng},
number = {1},
pages = {157-168},
publisher = {Association des Annales de l'Institut Fourier},
title = {Differentiation in lacunary directions and an extension of the Marcinkiewicz multiplier theorem},
url = {http://eudml.org/doc/74787},
volume = {38},
year = {1988},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 1
SP - 157
EP - 168
AB - We show that the maximal operator associated to the family of rectangles in ${\bf R}^ 3$ one of whose sides is parallel to $(1,2^ j,2^ k)$ for some j,k$\in {\bf H}Z$ is bounded on $L^ p$, $1&lt; p&lt; \infty $. We give an application of this theorem to obtain an extension of the Marcinkiewicz multiplier theorem.
LA - eng
KW - maximal operator; Marcinkiewicz multiplier theorem
UR - http://eudml.org/doc/74787
ER -