Abstract
We study Poletsky–Stessin Hardy spaces on complex ellipsoids in \(\mathbb {C}^{n}\). Different from one variable case, classical Hardy spaces are strictly contained in Poletsky–Stessin Hardy spaces on complex ellipsoids so boundary values are not automatically obtained in this case. We have showed that functions belonging to Poletsky–Stessin Hardy spaces have boundary values and they can be approached through admissible approach regions in the complex ellipsoid case. Moreover, we have obtained that polynomials are dense in these spaces. We also considered the composition operators acting on Poletsky–Stessin Hardy spaces on complex ellipsoids and gave conditions for their boundedness and compactness.
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Acknowledgments
This paper is based on the second part of my Ph.D. dissertation and I would like to express my sincere gratitude to my advisor Prof. Aydın Aytuna for his valuable guidance and support. I would also like to thank Prof. Evgeny A. Poletsky for the valuable discussions that we had during my visit at Syracuse University.
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Communicated by Heinrich Begehr.
Dedicated to Prof. Dr. Aydın Aytuna on the occasion of his 65th birthday.
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Şahin, S. Poletsky–Stessin Hardy Spaces on Complex Ellipsoids in \(\mathbb {C}^{n}\) . Complex Anal. Oper. Theory 10, 295–309 (2016). https://doi.org/10.1007/s11785-014-0440-9
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DOI: https://doi.org/10.1007/s11785-014-0440-9