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Weighted inequalities through factorization.

Eugenio Hernández (1991)

Publicacions Matemàtiques

In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined on X for which ||fw1/p||Lp(X) < ∞, where X is a measure space and w is a non-negative measurable function on X.It has recently...

Weighted-BMO and the Hilbert transform

Hui-Ming Jiang (1991)

Studia Mathematica

In 1967, E. M. Stein proved that the Hilbert transform is bounded from L to BMO. In 1976, Muckenhoupt and Wheeden gave an analogue of Stein’s result. They gave a necessary and sufficient condition for the boundedness of the Hilbert transform from L w . We improve the results of Muckenhoupt and Wheeden’s and give a necessary and sufficient condition for the boundedness of the Hilbert transform from B M O w to B M O w .

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