BOUNDEDNESS OF VOLTERRATYPE OPERATOR ON ANALYTIC MORREY SPACE
The Volterra operator is one of many important integral operator in functional analysis and operator theory. Volterra operator was first studied on Hilbert spaces L2[a, b] and by the time, Volterra operator has been considered on various function spaces. This thesis studies an integral operator T...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/49710 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | The Volterra operator is one of many important integral operator in functional
analysis and operator theory. Volterra operator was first studied on Hilbert spaces
L2[a, b] and by the time, Volterra operator has been considered on various function
spaces. This thesis studies an integral operator Tg defined on spaces of analytic
function on the unit disc D. The operator Tg with symbol g(z) of analytic function
on the unit disc, is defined by Tgf(z) =
R z
0 f(w)g?(w) dw. This operator generalized
the Volterra operator, that is, when g(z) = z. In addition, another integral
operator Ig defined as Igf(z) =
R z
0 f?(w)g(w) dw and the multiplication operator
Mgf(z) = f(z)g(z) are considered. The main purpose of this thesis is to find the
characterization of an analytic function g such that the integral operaor Tg and
Ig are bounded on analytic Morrey spaces. The analytic Morrey spaces could be
viewed as a complex version of the classical Morrey spaces. Furthermore, estimation
of the opertaor norm Tg and g are studied. The results of this thesis is then
compared with some previous related results about the characterization of operator
Tg and Ig on analytic function spaces. |
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