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Identifier 000441057
Title Closed Range Integral and Composition Operators on Spaces of Analytic Functions
Alternative Title Ολοκληρωτικοί τελεστές και τελεστές σύνθεσης με κλειστή εικόνα,σε χώρους αναλυτικών συναρτήσεων
Author Παντερής, Κωνσταντίνος
Thesis advisor Παπαδημητράκης, Μιχάλης
Reviewer Γαλανόπουλος, Πέτρος
Μίτσης, Θεμιστοκλής
Βετσάκος, Δημήτριος
Κωστάκης, Γεώργιος
Κολουντζάκης, Μιχαήλ
Σισκάκης, Αριστομένης
Abstract If X is a space of analytic functions f in D, the open unit disk, then the in¬tegral Sg and the composition Οφ operators on X are defined as Sgf (z) = J^f (w)g(w)dw and Οφ(f) = f ο φ respectively. This thesis is about find¬ing necessary and sufficient conditions for Sg and Οφ to have closed range or equivalently to be bounded below on some spaces of analytic functions. Four conditions for the integral operator Sg to have closed range on Hardy Hp(1 < p < oo), BMOA, Qp(0 < p < oo), and Besov Bp(1 < p < oo) spaces, respectively, are proved. All these conditions are based upon the behaviour of function g in the disk D. We also prove that, two already known conditions for Οφ to have closed range on Hardy space H2, can be extended to all Hardy spaces Hp, 0 < p < oo. The first condition concerns the behaviour of φ at the boundary of the disk D. The second one is based upon the behaviour of φ in the disk D and we prove this by using Hardy-Stein identities for one of the directions, and reverse Carleson measures and pull-back measures for the converse. Moreover, two necessary conditions and one sufficient condition, for Οφ to have the property of being bounded below on BMOA space, are presented.
Language English
Subject Function spaces
Ολοκληρωτικός τελεστής
Τελεστής σύνθεσης
Χώροι συναρτήσεων
Issue date 2021-07-23
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Doctoral theses
  Type of Work--Doctoral theses
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