On the (Formula presented.)-Hyperholomorphic Besov Space

Research output: Contribution to journalArticlepeer-review

Abstract

Let $$p>1$$p>1 and let $$\psi $$ψ be a structural set in $$\mathbb H$$H. This paper presents a seminormed $$\psi $$ψ-hyperholomorphic Besov space which satisfies the conformal covariant property preserving the “$$\psi $$ψ structure”. This is an analogue of what happens in the well-known one-dimensional complex Besov space, see Danikas (Function spaces and complex analysis, Joensuu 1997 (Ilomantsi) 935, 1999), Zhu (Operator theory in function spaces, 1990). These computations presented here are important complements to some results given in Cnops and Delanghe (Appl Anal 73:45–64, 1999) and Gürlebeck et al. (Complex Var Theory Appl 39:115–135, 1999) concerning to the theory of quaternionic right-linear space of $$\psi $$ψ-hyperholomorphic functions, see Shapiro and Vasilevski (Complex Var Theory Appl 27:17–46, 1995) and Shapiro and Vasilevski (Complex Var Theory Appl 27:67–96, 1995).

Original languageEnglish
Pages (from-to)1219-1227
Number of pages9
JournalComplex Analysis and Operator Theory
Volume9
Issue number5
DOIs
StatePublished - 18 Jun 2015

Keywords

  • Besov spaces
  • Quaternionic Möbius transformations
  • Quaternionic analysis

Fingerprint

Dive into the research topics of 'On the (Formula presented.)-Hyperholomorphic Besov Space'. Together they form a unique fingerprint.

Cite this