On the (Formula presented.)-Hyperholomorphic Besov Space

Research output: Contribution to journalArticle

Abstract

© 2014, Springer Basel. 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 languageAmerican English
Pages (from-to)1219-1227
Number of pages1096
JournalComplex Analysis and Operator Theory
DOIs
StatePublished - 18 Jun 2015

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Besov Spaces
Function Space
Psi Function
Operator Theory
Mathematical operators
Complex Analysis
Linear Space
Complement
Analogue

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title = "On the (Formula presented.)-Hyperholomorphic Besov Space",
abstract = "{\circledC} 2014, Springer Basel. 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 G{\"u}rlebeck 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).",
author = "{Gonz{\'a}lez Cervantes}, {Jos{\'e} Oscar}",
year = "2015",
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On the (Formula presented.)-Hyperholomorphic Besov Space. / González Cervantes, José Oscar.

In: Complex Analysis and Operator Theory, 18.06.2015, p. 1219-1227.

Research output: Contribution to journalArticle

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