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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