caa a22 4500 445836024 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s00209-009-0654-0 doi (NATIONALLICENCE)springer-10.1007/s00209-009-0654-0 Honzík Petr Institute of Mathematics, AS CR, Žitná 25, 115 67, Prague 1, Czech Republic aut On p dependent boundedness of singular integral operators [Elektronische Daten] [Petr Honzík] We study the classical Calderón Zygmund singular integral operator with homogeneous kernel. Suppose that Ω is an integrable function with mean value 0 on S 1. We study the singular integral operator $$T_\Omega f= {\rm p.v.} \, f * \frac {\Omega (x/|x|)}{|x|^2}.$$We show that for α >0 the condition $$\Bigg| \int \limits _{I} \Omega (\theta) \, d\theta \Bigg| \leq C |\log|I||^{-1-\alpha} \quad\quad\quad\quad (0.1)$$for all intervals |I|<1 in S 1 gives L p boundedness of T Ω in the range $${|1/2-1/p| < \frac \alpha {2(\alpha+1)}}$$ . This condition is weaker than the conditions from Grafakos and Stefanov (Indiana Univ Math J 47:455-469, 1998) and Fan etal. (Math Inequal Appl 2:73-81, 1999). We also construct an example of an integrable Ω which satisfies (0.1) such that T Ω is not L p bounded for $${|1/2-1/p| > \frac {3\alpha +1}{6(\alpha +1)}}$$ . Springer-Verlag, 2009 Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 931-937 0025-5874 267:3-4<931 2011 267 209 https://doi.org/10.1007/s00209-009-0654-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-009-0654-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Honzík Petr Institute of Mathematics, AS CR, Žitná 25, 115 67, Prague 1, Czech Republic aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 267/3-4(2011-04-01), 931-937 0025-5874 267:3-4<931 2011 267 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer