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Weighted inequalities for integral operators with some homogeneous kernels

Authors:

Maria Silvina Riveros Marta Urciuolo

Institution:

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

Abstract:

In this paper we study integral operators of the form

$Tf(x) = \smallint |x - a_1 y|^{ - \alpha _1 } ...|x - a_m y|^{ - \alpha _m } f(y)dy,$

₁ + ... +

_m = 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 ges

1 such that w(a _i x) les

cw(x) for a.e. x isin

ⁿ, 1

m. Moreover, we prove $\left\| {T\,f} \right\|_{BMO} \leqslant \left. c \right\|\left. f \right\|_\infty$ for a wide family of functions f isin

L (

ⁿ).Partially supported by CONICET, Agencia Cordoba Ciencia and SECYT-UNC.

Keywords:

weights integral operators

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