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Integral operators and weighted amalgams

C. Carton-LebrunH. HeinigS. Hofmann — 1994

Studia Mathematica

For large classes of indices, we characterize the weights u, v for which the Hardy operator is bounded from q ̅ ( L v p ̅ ) into 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 q ( L w p ) , 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.

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