Počet záznamů: 1

Method of rotations for bilinear singular integrals

  1. 1.
    0364816 - MU-W 2012 RIV US eng J - Článek v odborném periodiku
    Diestel, G. - Grafakos, L. - Honzík, Petr - Zengyan, S. - Terwilleger, E.
    Method of rotations for bilinear singular integrals.
    Communications in Mathematical Analysis. Roč. 3, - (2011), s. 99-107 ISSN 1938-9787.
    [Analysis, Mathematical Physics and Applications. Ixtapa, 01.03.2010-05.03.2010]
    Grant CEP: GA AV ČR KJB100190901
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: bilinear singular integrals * bilinear Hilbert transform * Fourier multipliers
    Kód oboru RIV: BA - Obecná matematika
    http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.cma/1298670006&page=record

    Suppose that $/Omega$ lies in the Hardy space $H^1$ of the unit circle $/mathbf S^{1}$ in $/mathbf R^2$. We use the Calderón-Zygmund method of rotations and the uniform boundedness of the bilinear Hilbert transforms to show that the bilinear singular operator with the rough kernel $/mathrm{p.v.} /, /Omega(x/|x|) |x|^{-2}$ is bounded from $L^p(/mathbf R)/times L^q(/mathbf R)$ to $L^r(/mathbf R)$, for a large set of indices satisfying $1/p+1/q=1/r$. We also provide an example of a function $/Omega$ in $L^q(/mathbf S^{ 1})$ with mean value zero to show that the singular integral operator given by convolution with $/mathrm{p.v.} /, /Omega(x/|x|) |x|^{-2}$ is not bounded from $L^{p_1}(/mathbf R)/times L^{p_2} (/mathbf R )$ to $ L^{p}(/mathbf R )$ for $1/2<p<1$, $1<p_1,p_2</infty$, $1/p_1+1/p_2=1/p$, $1/le q</infty$, and $1/p+1/q>2.
    Trvalý link: http://hdl.handle.net/11104/0200197
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