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INICIO |
27 de julio de 2024
Weighted inequalities through factorization.
| Título inglés | Weighted inequalities through factorization. |
|---|---|
| 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 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 been proved that the factorization of Ap weights is a particular case of a general factorization theorem concerning positive sublinear operators. The case in which the operator is bounded from Lp(X, v) to Lp(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 Lp(X, v) to Lq(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 Lp(X, v) to Lq(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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