ULTRACONTRACTIVITY AND STRONG SOBOLEV INEQUALITY FOR q-ORNSTEIN–UHLENBECK SEMIGROUP (-1 < q < 1)

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  • MAREK BOŻEJKO
    Instytut Matematyczny, Uniwersytet Wrocławski, Plac Grunwaldzki 2/4, 50-384 Wroclaw, Poland

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<jats:p> We prove that q-Ornstein–Uhlenbeck semigroup [Formula: see text] maps L<jats:sup>2</jats:sup> into L<jats:sup>∞</jats:sup> and [Formula: see text] for -1 < q < 1. This is an extension of Ph. Biane's<jats:sup>3</jats:sup> result on Nelson hypercontractivity and the ultracontractivity of the free (q=0) and q-second quantization. </jats:p>

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