A+ CATEGORY SCIENTIFIC UNIT

Integral operators and weighted amalgams

Volume 109 / 1994

C. Carton-Lebrun Studia Mathematica 109 (1994), 133-157 DOI: 10.4064/sm-109-2-133-157

Abstract

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.

Authors

  • C. Carton-Lebrun

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