Weighted sharp inequality for vector-valued multilinear integral operator (Q538020)

The author studies certain vector-valued multilinear integral operators which include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operators. He proves an important sharp inequality from which he obtaines that these operators are bounded on the weighted Lebesgue space \(L^p(w)\), \(1<p<\infty\), with \(w\in A_p\), and also bounded from a \(w\)-weighted \(L\log L\)-type space into the weighted weak-\(L^1(w)\) space with \(w\in A_1\).