Počet záznamů: 1

On p dependent boundedness of singular integral operators

  1. 1.
    0364813 - MU-W 2012 RIV DE eng J - Článek v odborném periodiku
    Honzík, Petr
    On p dependent boundedness of singular integral operators.
    Mathematische Zeitschrift. Roč. 267, 3-4 (2011), s. 931-937 ISSN 0025-5874
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: singular integral operators
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.749, rok: 2011
    http://www.springerlink.com/content/k507g30163351250/

    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).
    Trvalý link: http://hdl.handle.net/11104/0200195
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