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Pekka Koskela

  1. Characterizations of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces.

    Wed, 06/15/2011 - 15:01 — SomNambul
    Authors: Pekka Koskela, Yuan Zhou, Amiran Gogatishvili
    Subjects: Classical Analysis and ODEs
    Abstract

    On a metric measure space satisfying the doubling property, we establish
    several optimal characterizations of Besov and Triebel-Lizorkin spaces,
    including a pointwise characterization. Moreover, we discuss their
    (non)triviality under a Poincar\'e inequality.

  2. A Characterization of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions.

    Mon, 09/14/2009 - 09:01 — SomNambul
    Authors: Pekka Koskela, Dachun Yang, Yuan Zhou
    Subjects: Classical Analysis and ODEs
    Abstract

    In this paper, we establish the equivalence between the Haj{\l}asz-Sobolev
    spaces or classical Triebel-Lizorkin spaces and a class of grand
    Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are
    both doubling and reverse doubling. In particular, when $p\in(n/(n+1),\fz)$, we
    give a new characterization of the Haj{\l}asz-Sobolev spaces $\dot M^{1,
    p}(\rn)$ via a grand Littlewood-Paley function.

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