Method of rotations for bilinear singular integrals

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00364816" target="_blank" >RIV/67985840:_____/11:00364816 - isvavai.cz</a>
Alternative codes found
RIV/67985840:_____/11:00391049
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Method of rotations for bilinear singular integrals
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/KJB100190901" target="_blank" >KJB100190901: Singular and maximal operators on function spaces</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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