Integral operators and weighted amalgams
Studia Mathematica, Tome 109 (1994) no. 2, pp. 133-157
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from $ℓ^{q̅}(L^{p̅}_{v})$ into $ℓ^{q}(L^{p}_{u})$. 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 $ℓ^{q}(L^{p}_{w})$, 1 p,q ∞ , q ≠ p, $w ∈ A_p$, are also considered and sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator and local maximal operator in these spaces are obtained.
Keywords:
amalgam spaces, weights, $A_p$ weights, Hardy operator, Hardy-Littlewood maximal operator, weighted amalgam inequalities
Affiliations des auteurs :
C. Carton-Lebrun 1
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author = {C. Carton-Lebrun},
title = {Integral operators and weighted amalgams},
journal = {Studia Mathematica},
pages = {133--157},
publisher = {mathdoc},
volume = {109},
number = {2},
year = {1994},
doi = {10.4064/sm-109-2-133-157},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-109-2-133-157/}
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C. Carton-Lebrun. Integral operators and weighted amalgams. Studia Mathematica, Tome 109 (1994) no. 2, pp. 133-157. doi: 10.4064/sm-109-2-133-157
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