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This paper focuses on establishing boundedness properties and Parseval-Goldstein type relations for the generalized Mehler-Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math. , 18 (3): 235-287, 1967. Also, we derive an inversion formula for this transform over Lebesgue spaces.
Maan et al. (2024) studied this question.