Título inglés | Weighted inequalities through factorization. |
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Título español | Desigualdades ponderadas mediante factorización. |

Autor/es | Hernández, Eugenio |

Organización | Dep. Mat. Univ. Autón. Madrid, Madrid, España |

Revista | 0214-1493 |

Publicación | 1991, 35 (1): 141-153, 8 Ref. |

Tipo de documento | articulo |

Idioma | Inglés |

Resumen inglés | In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of A_{p} weights. We recall that a non-negative measurable function w on R^{n} is in the class A_{p}, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on L^{p}(R^{n}, w). In what follows, L^{p}(X, w) denotes the class of all measurable functions f defined on X for which ||fw^{1/p}||_{Lp(X)} < ∞, where X is a measure space and w is a non-negative measurable function on X.It has recently been proved that the factorization of A _{p} weights is a particular case of a general factorization theorem concerning positive sublinear operators. The case in which the operator is bounded from L^{p}(X, v) to L^{p}(Y, u), 1 < p < ∞, for u and v non-negative measurable functions on X and Y respectively, is treated in [8]. The case in which the operator is bounded from L^{p}(X, v) to L^{q}(X, u), 1 < p < q < ∞ is treated in [3].Our first result is a factorization theorem for weights u and v associated to operators bounded from L ^{p}(X, v) to L^{q}(Y, u) where X and Y are two, possibly different, measure spaces and p and q are any index between 1 and ∞. |

Código MathReviews | MR1103612 |

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