Главная

Carlos Perez

  1. End-point estimates for iterated commutators of multilinear singular integrals.

    Чт, 04/29/2010 - 15:01 — SomNambul
    Authors: Carlos Perez, Gladis Pradolini, Rodolfo Torres, Rodrigo Trujillo-Gonzalez
    Subjects: Classical Analysis and ODEs
    Abstract

    Iterated commutators of multilinear Calderon-Zygmund operators and pointwise
    multiplication with functions in $BMO$ are studied in products of Lebesgue
    spaces. Both strong type and weak end-point estimates are obtained, including
    weighted results involving the vectors weights of the multilinear
    Calderon-Zygmund theory recently introduced in the literature. Some better than
    expected estimates for certain multilinear operators are presented too.

  2. Sharp bounds for general commutators on weighted Lebesgue spaces.

    Пт, 02/12/2010 - 16:01 — SomNambul
    Authors: Daewon Chung, Carlos Perez, Cristina Pereyra
    Subjects: Classical Analysis and ODEs
    Abstract

    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 BMO 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 bound that is a power (k+1) of the
    A_2 constant of the weight. Sharp extrapolation provides corresponding L^p(w)
    estimates.

  3. The multilinear strong maximal function.

    Втр, 02/09/2010 - 16:01 — SomNambul
    Authors: Rodolfo H. Torres, Carlos Perez, Loukas Grafakos, Liguang Liu
    Subjects: Classical Analysis and ODEs
    Abstract

    A multivariable version of the strong maximal function is introduced and a
    sharp distributional estimate for this operator in the spirit of the Jessen,
    Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize
    the boundedness of this multivariable operator on products of weighted Lebesgue
    spaces equipped with multiple weights are obtained. Results for other
    multi(sub)linear maximal functions associated with bases of open sets are
    studied too.

  4. Sharp weighted estimates for classical operators.

    Втр, 01/26/2010 - 16:01 — SomNambul
    Authors: David Cruz-Uribe, Jose Maria Martell, Carlos Perez
    Subjects: Classical Analysis and ODEs
    Abstract

    We give a new proof of the sharp one weight $L^p$ inequality for any operator
    $T$ that can be approximated by Haar shift operators such as the Hilbert
    transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids
    the Bellman function technique and two weight norm inequalities. We use instead
    a recent result due to A. Lerner to estimate the oscillation of dyadic
    operators.

Math-arch

RSS-материал