# 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 language American English 1219-1227 1096 Complex Analysis and Operator Theory https://doi.org/10.1007/s11785-014-0431-x Published - 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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@article{548a10e7aac549cdb9589288727ced88,
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",
month = "6",
day = "18",
doi = "10.1007/s11785-014-0431-x",
language = "American English",
pages = "1219--1227",
journal = "Complex Analysis and Operator Theory",
issn = "1661-8254",
publisher = "Birkhauser Verlag Basel",

}

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

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the (Formula presented.)-Hyperholomorphic Besov Space

AU - González Cervantes, José Oscar

PY - 2015/6/18

Y1 - 2015/6/18

N2 - © 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).

AB - © 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).

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