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

Anthony Carbery

Type: Article

Publication Date: 1988-01-01

Citations: 44

DOI: https://doi.org/10.5802/aif.1127

Abstract

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.

Locations

French digital mathematics library (Numdam) - View - PDF
Annales de l’institut Fourier - View - PDF

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Works Cited by This (4)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations	1986	Michael Christ Javier Duoandikoetxea José L. Rubio de Francia
+ PDF Chat	Differentiation in lacunary directions	1978	Alexander Nagel E. M. Stein Stephen Wainger
+ PDF Chat	An almost-orthogonality principle with applications to maximal functions associated to convex bodies	1986	Anthony Carbery