Integral operators and weighted amalgams

Carton-Lebrun, C.; Heinig, H.; Hofmann, S.

Carton-Lebrun, C. ; Heinig, H. ; Hofmann, S.

Studia Mathematica, Tome 108 (1994), p. 133-157 / Harvested from The Polish Digital Mathematics Library

Résumé

For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from $ℓ^{q ̅} (L_{v}^{p ̅})$ into $ℓ^{q} (L_{u}^{p})$ . For more general operators of Hardy type, norm inequalities are proved which extend to weighted amalgams known estimates in weighted $L^{p}$ -spaces. Amalgams of the form $ℓ^{q} (L_{w}^{p})$ , 1 < p,q < ∞ , q ≠ p, $w \in A_{p}$ , are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.

Publié le : 1994-01-01

Zbl 0824.42015

EUDML-ID : urn:eudml:doc:216065

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     title = {Integral operators and weighted amalgams},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {133-157},
     zbl = {0824.42015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p133bwm}
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Carton-Lebrun, C.; Heinig, H.; Hofmann, S. Integral operators and weighted amalgams. Studia Mathematica, Tome 108 (1994) pp. 133-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p133bwm/

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