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Armen Vagharshakyan

  1. Recovering Singular Integrals from Haar Shifts.

    Mon, 11/30/2009 - 16:01 — SomNambul
    Authors: Armen Vagharshakyan
    Subjects: Classical Analysis and ODEs
    Abstract

    Any sufficiently smooth one-dimensional Calderon-Zygmund convolution operator
    is the average of Haar shift operators. The latter are dyadic operators which
    can be efficiently expressed in terms of the Haar basis. This extends the
    result of S. Petermichl on restoring Hilbert transform via Haar shift
    operators, a technique that has become fundamental to the analysis of these
    operators.

  2. Weak and Strong-type estimates for Haar Shift Operators: Sharp power on the $A_p$ characteristic.

    Thu, 11/05/2009 - 16:01 — SomNambul
    Authors: Tuomas P. Hytönen, Michael T. Lacey, Armen Vagharshakyan, Maria Carmen Reguera
    Subjects: Classical Analysis and ODEs
    Abstract

    As a corollary to our main result we deduce sharp A_p$ inequalities for

  3. A Three Dimensional Signed Small Ball Inequality.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Ioannis Parissis, Dmitriy Bilyk, Michael T. Lacey, Armen Vagharshakyan
    Subjects: Classical Analysis and ODEs
    Abstract

    The Small Ball Inequality is a conjectural lower bound on sums the L-infinity
    norm of sums of Haar functions supported on dyadic rectangles of a fixed volume
    in the unit cube. The conjecture is fundamental to questions in discrepancy
    theory, approximation theory and probability theory. In this article, we
    concentrate on a special case of the conjecture, and give the best known lower
    bound in dimension 3, using a conditional expectation argument.

  4. A Three Dimensional Signed Small Ball Inequality.

    Tue, 09/29/2009 - 15:21 — SomNambul
    Authors: Ioannis Parissis, Dmitriy Bilyk, Michael T. Lacey, Armen Vagharshakyan
    Subjects: Classical Analysis and ODEs
    Abstract

    The Small Ball Inequality is a conjectural lower bound on sums the L-infinity
    norm of sums of Haar functions supported on dyadic rectangles of a fixed volume
    in the unit cube. The conjecture is fundamental to questions in discrepancy
    theory, approximation theory and probability theory. In this article, we
    concentrate on a special case of the conjecture, and give the best known lower
    bound in dimension 3, using a conditional expectation argument.

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