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Czechoslovak Mathematical Journal

, Volume 55, Issue 2, pp 423–432 | Cite as

Weighted inequalities for integral operators with some homogeneous kernels

  • Maria Silvina Riveros
  • Marta Urciuolo
Article

Abstract

In this paper we study integral operators of the form
$$Tf(x) = \smallint |x - a_1 y|^{ - \alpha _1 } ...|x - a_m y|^{ - \alpha _m } f(y)dy,$$
α1 + ... + αm = n. We obtain the L p (w) boundedness for them, and a weighted (1, 1) inequality for weights w in A p satisfying that there exists c ⩾ 1 such that w(a i x) ⩽ cw(x) for a.e. x ∈ ℝn, 1 ⩽ im. Moreover, we prove \(\left\| {T\,f} \right\|_{BMO} \leqslant \left. c \right\|\left. f \right\|_\infty\) for a wide family of functions fL (ℝn).

Keywords

weights integral operators 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Maria Silvina Riveros
    • 1
  • Marta Urciuolo
    • 1
  1. 1.FaMAF Universidad Nacional de Cordoba, Ciem-CONICETCordoba

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