## Generalized Hardy–Cesaro operators between weighted spaces

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We characterize those non-negative, measurable functions ψ on [0, 1] and positive, continuous functions ω1 and ω2 on + for which the generalized Hardy-Cesàro operator defines a bounded operator Uψ: L 1(ω1) → L 1(ω2) This generalizes a result of Xiao [7] to weighted spaces. Furthermore, we extend Uψ to a bounded operator on M(ω1) with range in L 1(ω2) δ0, where M(ω1) is the weighted space of locally finite, complex Borel measures on +. Finally, we show that the zero operator is the only weakly compact generalized Hardy-Cesàro operator from L 1(ω1) to L 1(ω2).

Originalsprog Engelsk Glasgow Mathematical Journal 61 1 13-24 12 0017-0895 https://doi.org/10.1017/S0017089517000398 Udgivet - jan. 2019