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Hassan Ibrahim

  1. A remark on a generalization of a logarithmic Sobolev inequality to the Holder class.

    Tue, 08/25/2009 - 22:41 — SomNambul
    Authors: Hassan Ibrahim
    Subjects: Functional Analysis
    Abstract

    In a recent work of the author, a parabolic extension of the elliptic Ogawa
    type inequality has been established. This inequality is originated from the
    Brezis-Gallouet-Wainger logarithmic type inequalities revealing Sobolev
    embeddings in the critical case. In this paper, we improve the parabolic
    version of Ogawa inequality by allowing it to cover not only the class of
    functions from Sobolev spaces, but the wider class of Holder continuous
    functions.

  2. A critical parabolic Sobolev embedding via Littlewood-Paley decomposition.

    Fri, 08/14/2009 - 21:09 — SomNambul
    Authors: Hassan Ibrahim
    Subjects: Functional Analysis
    Abstract

    In this paper, we show a parabolic version of the Ogawa type inequality in
    Sobolev spaces. Our inequality provides an estimate of the $L^{\infty}$ norm of
    a function in terms of its parabolic $BMO$ norm, with the aid of the square
    root of the logarithmic dependency of a higher order Sobolev norm. The proof is
    mainly based on the Littlewood-Paley decomposition and a characterization of
    parabolic $BMO$ spaces.

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