Semyon B. Yakubovich, "On the Lebedev transformation in Hardy's spaces", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 194526, 14 pages, 2004. https://doi.org/10.1155/S0161171204301365
On the Lebedev transformation in Hardy's spaces
We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy's space , . This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space , , of analytic functions , in the strip . Boundedness and inversion properties of the Lebedev transformation from this space into the space are considered. When , we derive the familiar Plancherel theorem for the Kontorovich-Lebedev transform.
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