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Paul F.X. Mueller

  1. A Representation Theorem for Singular Integral Operators on Spaces of Homogeneous Type.

    Thu, 01/28/2010 - 16:01 — SomNambul
    Authors: Paul F.X. Mueller, Markus Passenbrunner
    Subjects: Functional Analysis
    Abstract

    Let (X,d,\mu) be a space of homogeneous type and E a UMD Banach space. Under
    the assumption mu({x})=0 for all x in X, we prove a representation theorem for
    singular integral operators on (X,d,mu) as a series of simple shifts and
    rearrangements plus two paraproducts. This gives a T(1) Theorem in this
    setting.

  2. Two Remarks on Primary Spaces.

    Tue, 11/03/2009 - 16:01 — SomNambul
    Authors: Paul F.X. Mueller
    Subjects: Functional Analysis
    Abstract

    We prove that for any operator $T$ on $ \ell^\infty(H^1 (\bT))$, the identity
    factores through $T$ or $\Id - T$.

    We re-prove analogous results of H.M. Wark for the spaces
    $\ell^infty(H^p(\bT))$, $1<p <\infty$. In the present paper direct
    combinatorics of colored dyadic intervals replaces the dependence on
    Szemeredi's theorem in the work of H. M. Wark.

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