INTEGRAL-OPERATORS ON WEIGHTED AMALGAMS

For large classes of indices, we characterize the weights u, upsilon for which the Hardy operator is bounded from l(qBAR)(L(upsilon)pBAR) 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 < infinity, q not-equal p, w is-an-element-of 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.