Generalized Hardy–Cesaro operators between weighted spaces
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Generalized Hardy–Cesaro operators between weighted spaces. / Pedersen, Thomas Vils.
In: Glasgow Mathematical Journal, Vol. 61, No. 1, 01.2019, p. 13-24.Research output: Contribution to journal › Journal article › Research › peer-review
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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
VL - 61
SP - 13
EP - 24
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
SN - 0017-0895
IS - 1
ER -
ID: 188910719