Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions

被引：30

作者：

Castillo Villalba, C. Marco Polo ^{[1
]}

Colombo, Fabrizio ^{[2
]}

Gantner, Jonathan ^{[3
]}

Oscar Gonzalez-Cervantes, J. ^{[4
]}

机构：

[1] Cuidad Univ, Inst Matemat, Unidad Posgrad, Mexico City 04510, DF, Mexico

[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[3] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[4] IPN, Dept Matemat, ESFM, Mexico City 07338, DF, Mexico

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2015年 / 9卷 / 02期

关键词：

Bloch spaces; Besov spaces; Dirichlet spaces; Slice hyperholomorphic functions; NONCOMMUTING OPERATORS; CALCULUS;

D O I：

10.1007/s11785-014-0380-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Mobius maps by using a suitable notion of composition.

引用

页码：479 / 517

页数：39

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