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 -