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From Hankel Operators to Carleson Measures in a Quaternionic Variable

Part of: Generalized function theory Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  17 July 2017

Nicola Arcozzi  and
Giulia Sarfatti
Nicola Arcozzi
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy ([email protected]; [email protected])
Giulia Sarfatti
Affiliation:
Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy ([email protected]; [email protected])
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Abstract

We introduce and study Hankel operators defined on the Hardy space of regular functions of a quaternionic variable. Theorems analogous to those of Nehari and Fefferman are proved.

Keywords

Hardy space on the quaternionic ballfunctions of a quaternionic variableHankel operators

MSC classification

Secondary: 30G35: Functions of hypercomplex variables and generalized variables 46E22: Hilbert spaces with reproducing kernels (= 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 565 - 585
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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References

1. Alpay, D., Colombo, F. and Sabadini, I., Self-mappings of the quaternionic unit ball: multiplier properties, Schwarz–Pick inequality and Nevanlinna–Pick interpolation problem, Indiana Univ. Math. J. 64 (2015), 151–180.Google Scholar
2. Ambrosio, L., Fusco, N. and Pallara, D., Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs (Clarendon Press, Oxford, 2000).CrossRefGoogle Scholar
3. Arcozzi, N. and Sarfatti, G., Invariant metrics for the quaternionic Hardy space, J. Geom. Analysis 25 (2015), 2028–2059.CrossRefGoogle Scholar
4. Brackx, F., Delanghe, R. and Sommen, F., Clifford analysis (Pitman, Boston, MA, 1982).Google Scholar
5. Carleson, L., Interpolations by bounded analytic functions and the corona problem, Annals Math. 76 (1962), 547–559.CrossRefGoogle Scholar
6. Coifman, R. R., Rochberg, R. and Weiss, G., Factorization theorems for Hardy spaces in several variables, Annals Math. 103 (1976), 611–635.CrossRefGoogle Scholar
7. De Fabritiis, C., Gentili, G. and Sarfatti, G., Quaternionic Hardy spaces, Annali Sc. Norm. Sup. Pisa Cl. Sci. (2017), in press.CrossRefGoogle Scholar
8. Duren, P. L., Theory of Hp spaces, Pure and Applied Mathematics, Volume 38 (Academic Press, 1970).Google Scholar
9. Fefferman, C. and Stein, E. M., Hp spaces of several variables, Acta Math. 129 (1972), 137–193.CrossRefGoogle Scholar
10. Gentili, G. and Struppa, D. C., A new theory of regular functions of a quaternionic variable, Adv. Math. 216 (2007), 279–301.CrossRefGoogle Scholar
11. Gentili, G., Stoppato, C. and Struppa, D. C., Regular functions of a quaternionic variable, Springer Monographs in Mathematics (Springer, 2013).CrossRefGoogle Scholar
12. Ghiloni, R., Moretti, V. and Perotti, A., Continuous slice functional calculus in quaternionic Hilbert spaces, Rev. Math. Phys. 25 (2013), 1350006.CrossRefGoogle Scholar
13. Nehari, Z., On bounded bilinear forms, Annals Math. 65 (1957), 153–162.CrossRefGoogle Scholar
14. Peller, V. V., An excursion into the theory of Hankel operators, in Holomorphic spaces, Mathematical Sciences Research Institute Publications, Volume 33, pp. 65–130 (Cambridge University Press, 1998).Google Scholar
15. Zhu, K., Operator theory in function spaces, Monographs and Textbooks in Pure and Applied Mathematics, Volume 139 (Marcel Dekker, 1990).Google Scholar