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On slice hyperholomorphic fractional Hardy spaces
Author(s) -
Alpay Daniel,
Colombo Fabrizio,
Sabadini Irene
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201700011
Subject(s) - mathematics , hardy space , unit sphere , hilbert space , pure mathematics , reproducing kernel hilbert space , factorization , space (punctuation) , unit (ring theory) , kernel (algebra) , algebra over a field , mathematical analysis , algorithm , mathematics education , computer science , operating system
In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss their properties of invariance and of factorization in terms of functions in the Hardy space of the half space in the first case, and in terms of a suitable reproducing kernel Hilbert space in the case of the unit ball.