C. Pereyra

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The existence of a bounded inverse of (I ? b) on L p ((b is the dyadic paraproduct) does not imply the same for (I ? b), ?1 < 1 (we present a counterexample); but it guarantees the existence of 1 < po such that there exist a bounded inverse in L po for every ?1 1. This is equivalent to showing that the RH d p class of weights is not preserved under certain(More)
We show that if an operator T is bounded on weighted Lebesgue space L 2 (w) and obeys a linear bound with respect to the A 2 constant of the weight, then its commutator [b, T ] with a function b in BM O will obey a quadratic bound with respect to the A 2 constant of the weight. We also prove that the kth-order commutator T k b = [b, T k−1 b ] will obey a(More)
We extend the definitions of dyadic paraproduct and t-Haar multipliers to dyadic operators that depend on the complexity (m, n), for m and n natural numbers. We use the ideas developed by Nazarov and Volberg in [NV] to prove that the weighted L 2 (w)-norm of a paraproduct with complexity (m, n), associated to a function b ∈ BM O d , depends linearly on the(More)
The dyadic paraproduct is bounded in weighted Lebesgue spaces Lp(w) if and only if the weight w belongs to the Muckenhoupt class A d p. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the simplest L2(w) case. In this paper we prove the linear bound on the norm of the dyadic paraproduct in the weighted Lebesgue space(More)
Decompressive craniectomy (DC) is a surgical practice that has been used since the late 19th century. The cerebral blood flow increase after the performance of a DC can delay and even prevent the development of cerebral circulatory arrest and brain death (BD). We aimed to determine the prevalence of BD, the use of DC, and the evolution to BD with versus(More)
We show that if a weight w ∈ C d 2t and there is q > 1 such that w 2t ∈ A d q , then the L 2-norm of the t-Haar multiplier of complexity (m, n) associated to w depends on the square root of the C d 2t-characteristic of w times the square root A d q-characteristic of w 2t times a constant that depends polynomially on the complexity. In particular, if w ∈ C d(More)