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 APM  Vol.10 No.9 , September 2020
A Growth Behavior of Szegö Type Operators
Abstract: We define new integral operators on the Haydy space similar to Szegö projection. We show that these operators map from Hp to H2 for some 1 ≤ p < 2, where the range of p is depending on a growth condition. To prove that, we generalize the Hausdorff-Young Theorem to multi-dimensional case.
Cite this paper: Yang, J. (2020) A Growth Behavior of Szeg&#246; Type Operators. Advances in Pure Mathematics, 10, 492-500. doi: 10.4236/apm.2020.109030.
References

[1]   Rudin, W. (2008) Function Theory in the Unit Ball of Cn. Springer-Verlag, Berlin.

[2]   Zhu, K. (2005) Spaces of Holomorphic Functions in the Unit Ball. Springer-Verlag, New York.

[3]   Duren, P. and Schuster, A. (2004) Bergman Spaces. American Mathematical Society, Providence, RI.
https://doi.org/10.1090/surv/100

[4]   Bennett, C. and Sharpley, R. (1988) Interpolation of Operators. Academic Press, Boston.

[5]   Yang, J. (2015) Norm Convergent Partial Sums of Taylor Series. Bulletin of the Korean Mathematical Society, 52, 1729-1735.
https://doi.org/10.4134/BKMS.2015.52.5.1729

 
 
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