On p dependent boundedness of singular integral operators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00364813" target="_blank" >RIV/67985840:_____/11:00364813 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00209-009-0654-0" target="_blank" >http://dx.doi.org/10.1007/s00209-009-0654-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-009-0654-0" target="_blank" >10.1007/s00209-009-0654-0</a>

Result language
angličtina
Original language name
On p dependent boundedness of singular integral operators
Original language description
We study the classical Caldern Zygmund singular integral operator with homogeneous kernel. Suppose that Omega is an integrable function with mean value 0 on S (1). We study the singular integral operator T(Omega)f = p.v f * Omega(x/vertical bar chi vertical bar)/vertical bar chi vertical bar(2). We show that for alpha > 0 the condition vertical bar integral(I) Omega(theta) d theta vertical bar <= C vertical bar log vertical bar vertical bar I vertical bar vertical bar(-1-alpha) (0.1) for all intervals |I| < 1 in S (1) gives L (p) boundedness of T (Omega) in the range vertical bar 1/2-1/p vertical bar < alpha/2(alpha+1). This condition is weaker than the conditions from Grafakos and Stefanov (Indiana Univ Math J 47:455-469, 1998) and Fan et al. (Math Inequal Appl 2:73-81, 1999). We also construct an example of an integrable Omega which satisfies (0.1) such that T (Omega) is not L (p) bounded for vertical bar 1/2-1/p vertical bar > 3 alpha+1/6(alpha+1).
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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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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