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Artículo
The L(log L)e endpoint estimate for maximal singular integral operators
(Elsevier, 2015-08-01)
We prove in this paper the following estimate for the maximal operator T ∗ associated to the singular integral operator T: kT ∗ fkL 1,∞ (w) . 1 ǫ Z Rn | f(x)| ML(log L) ǫ (w)(x) dx, w ≥ 0, 0 < ǫ ≤ 1. This ...
Artículo
Optimal exponents in weighted estimates without examples
(International Press, 2015)
t. We present a general approach for proving the optimality of the exponents on weighted estimates. We show that if an operator T satisfies a bound like kT kLp(w) ≤ c [w] β Ap w ∈ Ap, then the optimal lower bound ...
Artículo
Exponential decay estimates for singular integral operators
(Springer, 2013-12)
The following subexponential estimate for commutators is proved |{x ∈ Q : |[b, T]f(x)| > tM2 f(x)}| ≤ c e− √ α tkbkBMO |Q|, t > 0. where c and α are absolute constants, T is a Calder´on–Zygmund operator, M is the Hardy ...
Artículo
Sharp bounds for general commutators on weighted Lebesgue spaces
(American Mathematical Society, 2012)
We show that if a linear operator T is bounded on weighted Lebesgue space L2(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a ...
Artículo
A new quantitative two weight theorem for the Hardy-Littlewood maximal operator
(American Mathematical Society, 2015-02)
A quantitative two weight theorem for the Hardy-Littlewood maximal operator is proved improving the known ones. As a consequence a new proof of the main results in [HP] and in [HPR12] is obtained which avoids the use of ...