Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces
We characterize the integration operators V g with symbol g for which V g acts as an absolutely summing operator on weighted Bloch spaces B β and on weighted Bergman spaces A α p . We show that V g is r -summing on A α p , 1 ≤ p < ∞ , if and only if g belongs to a suitable Besov space. We also sh...
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Published in | Integral equations and operator theory Vol. 96; no. 1; p. 1 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.03.2024
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
ISSN | 0378-620X 1420-8989 |
DOI | 10.1007/s00020-023-02742-7 |
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Summary: | We characterize the integration operators
V
g
with symbol
g
for which
V
g
acts as an absolutely summing operator on weighted Bloch spaces
B
β
and on weighted Bergman spaces
A
α
p
. We show that
V
g
is
r
-summing on
A
α
p
,
1
≤
p
<
∞
, if and only if
g
belongs to a suitable Besov space. We also show that there is no non trivial nuclear Volterra operators
V
g
on Bloch spaces and on Bergman spaces. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
ISSN: | 0378-620X 1420-8989 |
DOI: | 10.1007/s00020-023-02742-7 |