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  • Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in ▫$L^p(\mathbb C)$▫
    Dragičević, Oliver ; Volberg, Alexander
    We prove a new Littlewood-Paley type inequality for heat extensions on the plane. Its main consequence regards the well-known conjecture of Iwaniec about the ▫$L^p$▫-norm of the Ahlfors-Beurling ... operator. We show that the current best result can be improved asymptoticaly when ▫$p \to \infty$▫ by a factor of ▫$\sqrt{2}$▫, and bya factor of 2 for real-valued functions. The latter estimate is the best possible, i.e., in asymptotical sense for large ▫$p$▫ and for real functions, the Iwaniec conjecture holds.
    Source: Indiana University mathematics journal. - ISSN 0022-2518 (Vol. 54, no. 4, 2005, str. 971-996)
    Type of material - article, component part
    Publish date - 2005
    Language - english
    COBISS.SI-ID - 14139737

    Link(s):

    http://dx.doi.org/10.1512/iumj.2005.54.2554

source: Indiana University mathematics journal. - ISSN 0022-2518 (Vol. 54, no. 4, 2005, str. 971-996)

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