Back to my home page
María de los Ángeles Alfonseca-Cubero
-
Publications:
Strong type
inequalities and an almost-orthogonality principle for
families of maximal operators along directions in R2, J. London Math. Soc. (2) 67 (2003),
208-218.
Abstract: The paper proves an almost-orthogonality principle
for maximal operators over arbitrary sets of directions in
R2. Namely, the Lp-bounds for an operator of this
type are obtained 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.
Applications to several types of maximal operators are provided.
A remark on
maximal operators along directions in R2,
(with F. Soria and A. Vargas) Math. Res. Lett. 10 (2003), no. 1,
41-49.
Abstract: In this paper we give a simple proof of a
long-standing conjecture, recently proved by N. Katz, on the
weak-type norm of a maximal operator associated with an arbitrary
collection of directions in the plane. The proof relies upon a
geometric argument (a weak-type almost-orthogonality principle)
and on induction with respect to the number of directions.
Applications are given to estimate the behavior of several types
of maximal operators.
An
almost-orthogonality principle in L2 for directional
maximal functions (with
F. Soria and A. Vargas), Harmonic Analysis at Mount Holyoke, 1-7, Contemp.
Math, 320 Amer. Math. Soc. 2003.
Abstract: In this work we improve our result in the previous paper.
We prove a strong-type almost-orthogonality principle in L2 for
maximal functions along several directions. We use geometric
methods and a covering lemma.