Generalized Hardy–Cesaro operators between weighted spaces

TY - JOUR

T1 - Generalized Hardy–Cesaro operators between weighted spaces

AU - Pedersen, Thomas Vils

PY - 2019/1

Y1 - 2019/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85057741111&partnerID=8YFLogxK

U2 - 10.1017/S0017089517000398

DO - 10.1017/S0017089517000398

M3 - Journal article

SN - 0017-0895

VL - 61

SP - 13

EP - 24

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

IS - 1

ER -