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STRONG TYPE INEQUALITIES AND AN ALMOST-ORTHOGONALITY PRINCIPLE FOR FAMILIES
 

Summary: STRONG TYPE INEQUALITIES AND AN
ALMOST-ORTHOGONALITY PRINCIPLE FOR FAMILIES
OF MAXIMAL OPERATORS ALONG DIRECTIONS IN R2
ANGELES ALFONSECA
Abstract. In this paper we prove an almost-orthogonality principle for
maximal operators over arbitrary sets of directions in R2
. Namely, we
obtain Lp
-bounds for an operator of this type from the corresponding
Lp
-bounds of the maximal functions associated to a certain partition of
the set of directions, and from the particular structure of this partition.
We give applications to several types of maximal operators.
1. Introduction
In this paper we continue the study of maximal functions along directions
in R2, initiated in [1] in connection with a certain notion of `planar' almost-
orthogonality.
Let 0 be an ordered subset of [0,
4 ). We denote its elements by 1, 2, . . .,
with

  

Source: Alfonseca-Cubero, Maria - Department of Mathematics, North Dakota State University

 

Collections: Mathematics