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Weighted inequalities for integral operators with some homogeneous kernels

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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 ⩽ i ⩽ m. Moreover, we prove \(\left\| {T\,f} \right\|_{BMO} \leqslant \left. c \right\|\left. f \right\|_\infty\) for a wide family of functions f ∈ L ∞ (ℝn).

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Authors and Affiliations

  1. FaMAF Universidad Nacional de Cordoba, Ciem-CONICET, Ciudad Universitaria, 5000, Cordoba

    Maria Silvina Riveros & Marta Urciuolo

Authors
  1. Maria Silvina Riveros
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  2. Marta Urciuolo
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Partially supported by CONICET, Agencia Cordoba Ciencia and SECYT-UNC.

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Riveros, M.S., Urciuolo, M. Weighted inequalities for integral operators with some homogeneous kernels. Czech Math J 55, 423–432 (2005). https://doi.org/10.1007/s10587-005-0032-y

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  • DOI: https://doi.org/10.1007/s10587-005-0032-y

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