Abstract
This paper is concerned with generalizations of the classical Hardy spaces (8, p. 39) and the question of boundary values for functions of these various spaces. The general setting is the “big disk” Δ discussed by Arens and Singer in (1, 2) and by Hoffman in (7). Analytic functions are defined in (1). Classes of such functions corresponding to the Hardy Hp spaces are considered and shown to possess boundary values in (2). Contrary to the classical case, such functions do not form a Banach space; hence they are not the functional analytic analogue of the classical spaces. In (3) quasi-analytic functions are defined while in (4) Hardy spaces of such functions are considered and are shown to have boundary values and to form a Banach space.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
