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PureMathematicsnØêÆ,2021,11(9),1643-1648
PublishedOnlineSeptember2021inHans.http://www.hanspub.org/journal/pm
https://doi.org/10.12677/pm.2021.119182
l•êBergman˜mA
p
ψ
Bloch˜m
VolterraÈ©Žf
–––’’’¤¤¤§§§¯¯¯
∗
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•êBergman˜m§Bloch˜m§Volterra.Žf§k.5
VolterraTypeOperatorsfromBergman
SpaceswithExponentialWeightstothe
BlochSpace
YechengShi,ErminWang
∗
SchoolofMathematicsandStatistics,LingnanNormalUniversity,ZhanjiangGuangdong
Received:Aug.8
th
,2021;accepted:Sep.10
th
,2021;published:Sep.17
th
,2021
∗ÏÕŠö"
©ÙÚ^:–’¤,¯.l•êBergman˜mA
p
ψ
Bloch˜mVolterraÈ©Žf[J].nØêÆ,2021,11(9):
1643-1648.DOI:10.12677/pm.2021.119182
–’¤§¯
Abstract
WeconsidertheboundednessandcompactnessofVolterratypeoperatorsfromthe
BergmanspaceswithexponentialweightstotheBlochSpace.
Keywords
BergmanSpaceswithExponentialWei ghts,BlochSpace,VolterraTypeOperators,
Boundedness
Copyright
c
2021byauthor(s)andHansPublishersInc.
This work is licensed undertheCreative Commons Attribution International License (CCBY 4.0).
http://creativecommons.org/licenses/by/4.0/
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DOI:10.12677/pm.2021.1191821644nØêÆ
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kk
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DOI:10.12677/pm.2021.1191821645nØêÆ
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(z) <∞.
DOI:10.12677/pm.2021.1191821646nØêÆ
–’¤§¯
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(1−|z|
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)|g
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(z)|e
ψ(z)
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p,z
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<∞.
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0
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: A
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p
(z) = 0.
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1−
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p
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(w),Kkk
p,z
k
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0 =lim
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g
k
p,z
k
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|z|→1
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(w)|
&lim
|z|→1
(1−|z|
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p,z
(z)|
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|z|→1
(1 −|z|
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(z)|e
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−
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p
(z)=0,Ké?¿>0,•3r
0
∈(0,1),¦
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(1−|z|
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−
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…ρ>0,¤±|z|≤r
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ψ(z)
ρ
−
2
p
(z)<
∞k..ld½n3.1,T
g
: A
p
ψ
→B´.Žf.…·‚•,•3êM,¦
M:=sup
|w|≤r
0
(1−|w|
2
)|g
0
(w)|<∞.
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n
}•A
p
ψ
¥k.S,…3D;f8þ˜—Âñu0.K
kT
g
f
n
k
B
=sup
w∈D
(1−|w|
2
)|g
0
(w)|f
n
(w)|
=sup
|w|≤r
0
(1−|w|
2
)|g
0
(w)|f
n
(w)|+sup
|w|>r
0
(1−|w|
2
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0
(w)|f
n
(w)|
.M|f
n
(w)|+sup
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0
(1−|w|
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A
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.M|f
n
(w)|+
DOI:10.12677/pm.2021.1191821647nØêÆ
–’¤§¯
Ïd,n→∞ž,kT
g
f
n
k
B
→0.¤±T
g
: A
p
ψ
→B´k;Žf.
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ë•©z
[1]Hu, Z.,Lv,X.and Schuster, A.(2019) BergmanSpaces withExponential Weights.Journalof
FunctionalAnalysis,276,1402-1429.https://doi.org/10.1016/j.jfa.2018.05.001
[2]Pommerenke,C.(1977)SchlichteFunktionenundanalytischeFunktionenvonbeschr¨ankter
mittlererOszillation.CommentariiMathematiciHelvetici,52,591-602.
https://doi.org/10.1007/BF02567392
[3]Li,S.(2008)VolterraCompositionOperatorsbetweenWeightedBergmanSpacesandBloch
TypeSpaces.JournaloftheKoreanMathematicalSociety,45,229-248.
https://doi.org/10.4134/JKMS.2008.45.1.229
[4]Û§u,¡¸,4©.•êBergman˜mA
p
ϕ
ÚA
∞
ϕ
mTeoplitzŽf[J].êÆÆ,2021,
64(4):655-668.
DOI:10.12677/pm.2021.1191821648nØêÆ

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