Angular derivatives and boundary values of H(b) spaces of unit ball of ℂn. Issue 2 (1st February 2021)

• Record Type: Journal Article
• Authors: Şahin, Sibel
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 2(2021)
• Page Start: 226
• Page End: 237
• Publication Date: 2021-02-01
• Subjects: H. Boas; deBranges–Rovnyak spaces -- angular derivatives -- Clark measures -- admissible boundary limits; 32A37 (primary) -- 32A35 -- 32A40 (secondary); Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1715373
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : In this work, deBranges–Rovnyak spaces, H ( b ), on the unit ball of C n are studied. An integral representation of the functions in H ( b ) through the Clark measure on S n associated with b is given and a characterization of admissible boundary limits is given in relation with finite angular derivatives. Lastly, the interplay between Clark measures and angular derivatives is examined and it is obtained that Clark measure associated with b has an atom at a boundary point if and only if b has finite angular derivative at the same point.