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On p dependent boundedness of singular integral operators
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SYSNO ASEP 0364813 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On p dependent boundedness of singular integral operators Author(s) Honzík, Petr (MU-W) RID, SAI Source Title Mathematische Zeitschrift. - : Springer - ISSN 0025-5874
Roč. 267, 3-4 (2011), s. 931-937Number of pages 7 s. Language eng - English Country DE - Germany Keywords singular integral operators Subject RIV BA - General Mathematics CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000288261600021 EID SCOPUS 79952572756 DOI 10.1007/s00209-009-0654-0 Annotation 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). Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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