Sergei Treil

  1. Carleson--Buckley measures beyond the scope of $A_\infty$ and their applications.

    Authors: Sergei Treil, Alexander Volberg, Fedor Nazarov, Alexander Reznikov
    Subjects: Classical Analysis and ODEs
    Abstract

    Carleson measures are ubiquitous in Harmonic Analysis. In the paper of
    Fefferman--Kenig--Pipher in 1991 an interesting class of Carleson measures was
    introduced for the need of regularity problems of elliptic PDE. These Carleson
    measures were associated with $A_\infty$ weights. In discrete setting (we need
    exactly discrete setting here) they were studied by Buckley's, where they were
    associated with dyadic $A\infty^d$. Our goal here is to show that such
    Carleson--Buckley measures (in discrete setting) exists for virtually any
    positive function (weight).

  2. Weak-star convergence in multiparameter Hardy spaces.

    Authors: Jill Pipher, Sergei Treil
    Subjects: Classical Analysis and ODEs
    Abstract

    We prove a multiparameter version of a classical theorem of Jones and Journe
    on weak-star convergence in the Hardy space $H^1$.

  3. Weak-star convergence in multiparameter Hardy spaces.

    Authors: Jill Pipher, Sergei Treil
    Subjects: Classical Analysis and ODEs
    Abstract

    We prove a multiparameter version of a classical theorem of Jones and Journe
    on weak-star convergence in the Hardy space $H^1$.

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