Department of Mathematics
Library of the School of Science

2022-03-23

2022

Kioulafa Kyranna

Αλέκος Βίδρας Καθηγητής Πανεπιστημίου Κύπρου
Απόστολος Γιαννόπουλος Καθηγητής ΕΚΠΑ
Αριστείδης Κοντογεώργης Καθηγητής ΕΚΠΑ
Σοφοκλής Μερκουράκης Καθηγητής ΕΚΠΑ
Βασίλειος Νεστορίδης Καθηγητής ΕΚΠΑ
Αριστομένης Συσκάκης Καθηγητής ΑΠΘ
Τηλέμαχος Χατζηαφράτης Καθηγητής ΕΚΠΑ

Ολοκληρώματα τύπου Cauchy

English

Cauchy type integrals

In this work we present several results concerning mostly applications of Baire’s Category theorem in Complex Analysis in one and in several complex variables. An important problem in complex analysis is whether there exists a holomorphic function f, in a given open set Ω in C^n , which is singular at every boundary point of Ω. Also the problem of constructing singular functions with specific properties – for example satisfying certain growth conditions near the boundary or having certain smoothness upto the boundary – has been studied in various directions. In this work we will show – under certain restrictions on the open set – that the set of the OL^p (holomorphic and L^p with respect to Lebesgue measure) and H^p (holomorphic and H^p with respect to the Euclidean surface area measure on the sphere ), 1 ≤ p ≤∞ , functions in Ω and B , which are totally unbounded, is dense and Gδ in the space OL ^ p (Ω) and H ^ p(B) respectively. In fact we work mostly with the spaces ∩OL^p(Ω),p