## Generalized Hardy–Cesaro operators between weighted spaces

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#### Standard

Generalized Hardy–Cesaro operators between weighted spaces. / Pedersen, Thomas Vils.

I: Glasgow Mathematical Journal, Bind 61, Nr. 1, 01.2019, s. 13-24.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

#### Harvard

Pedersen, TV 2019, 'Generalized Hardy–Cesaro operators between weighted spaces', Glasgow Mathematical Journal, bind 61, nr. 1, s. 13-24. https://doi.org/10.1017/S0017089517000398

#### APA

Pedersen, T. V. (2019). Generalized Hardy–Cesaro operators between weighted spaces. Glasgow Mathematical Journal, 61(1), 13-24. https://doi.org/10.1017/S0017089517000398

#### Vancouver

Pedersen TV. Generalized Hardy–Cesaro operators between weighted spaces. Glasgow Mathematical Journal. 2019 jan;61(1):13-24. https://doi.org/10.1017/S0017089517000398

#### Author

Pedersen, Thomas Vils. / Generalized Hardy–Cesaro operators between weighted spaces. I: Glasgow Mathematical Journal. 2019 ; Bind 61, Nr. 1. s. 13-24.

#### Bibtex

@article{f849b1a564974bd78158f61a8a9be40c,
title = "Generalized Hardy–Cesaro operators between weighted spaces",
abstract = "We characterize those non-negative, measurable functions ψ on [0, 1] and positive, continuous functions ω1 and ω2 on + for which the generalized Hardy-Ces{\a}ro 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-Ces{\a}ro operator from L 1(ω1) to L 1(ω2).",
author = "Pedersen, {Thomas Vils}",
year = "2019",
month = "1",
doi = "10.1017/S0017089517000398",
language = "English",
volume = "61",
pages = "13--24",
journal = "Glasgow Mathematical Journal",
issn = "0017-0895",
publisher = "Cambridge University Press",
number = "1",

}

#### RIS

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