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SEMINARI D’ANALISI
DE BARCELONA
Curs 2014–2015
Dilluns 16 de mar¸c del 2015, 15:00h
Aula Petita (CRM)
Universitat Aut`onoma de Barcelona
http://mat.uab.cat/ Analisi/wordpress/
Universitat de Barcelona
Quantitative estimates for dyadic shifts
and applications in Calder´
on-Zygmund theory
JOSE MANUEL CONDE
ICMAT
ABSTRACT:
In this talk, we prove the following pointwise estimate:
0
Am
S f (x) . (m + 1)AS 0 f (x)
where the operators Am
S are positive dyadic shifts of complexity m ≥ 0 defined by
X 1 Z
Am
f
(x)
:=
f
(y)dy
χQ (x).
S
|Q(m) | Q(m)
Q∈S⊂D
It turns out that this inequality involving dyadic models of singular integrals can be used to give a
pointwise estimate for Calder´
on-Zygmund operators. In turn, this allows to answer a question posed
by A. Lerner regarding the domination of singular integrals by simpler dyadic-like operators in quasiBanach spaces. Several applications to weighted estimates for both multilinear Calder´on-Zygmund
operators and square functions will be discussed.
Joint work with Guillermo Rey.
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