Korean J. Math. Vol. 33 No. 1 (2025) pp.7-19
DOI: https://doi.org/10.11568/kjm.2025.33.1.7-19

Generalized hilbert operator on bergman spaces

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Published: Mar 30, 2025
Keywords:
Hilbert Operator, Hypergeometric Functions, Bergman Spaces
Mathematics Subject Classification:
30E20, 30H20, 31B10, 33C05

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Simi Bhuyan
epartment of Applied Sciences, Gauhati University, Guwahati, Assam 781014, India
Sunanda Naik
Department of Applied Sciences, Gauhati University, Guwahati, Assam 781014, India

Abstract

We consider the generalized Hilbert operator Hβ for β≥0 and find the condition on the parameter β for which the operator Hβ is bounded on the Bergman space Ap for 2<p<∞. Also, we estimates the upper bound of the norm on Ap. Further shows that Hβ is not bounded on A2 for 0≤β<1.



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Gauhati University

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