# Weighted inequalities through factorization.

Publicacions Matemàtiques (1991)

- Volume: 35, Issue: 1, page 141-153
- ISSN: 0214-1493

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topHernández, Eugenio. "Weighted inequalities through factorization.." Publicacions Matemàtiques 35.1 (1991): 141-153. <http://eudml.org/doc/41680>.

@article{Hernández1991,

abstract = {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 ∞.},

author = {Hernández, Eugenio},

journal = {Publicacions Matemàtiques},

keywords = {weighted inequalities; factorization theorem for weights; integral transform; Hardy operator; fractional integrals; Laplace transform; Riemann-Liouville operator},

language = {eng},

number = {1},

pages = {141-153},

title = {Weighted inequalities through factorization.},

url = {http://eudml.org/doc/41680},

volume = {35},

year = {1991},

}

TY - JOUR

AU - Hernández, Eugenio

TI - Weighted inequalities through factorization.

JO - Publicacions Matemàtiques

PY - 1991

VL - 35

IS - 1

SP - 141

EP - 153

AB - 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 ∞.

LA - eng

KW - weighted inequalities; factorization theorem for weights; integral transform; Hardy operator; fractional integrals; Laplace transform; Riemann-Liouville operator

UR - http://eudml.org/doc/41680

ER -

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