Index transforms associated with products of Whittakerʹs functions

Integral transformations with respect to parameters of the products of Whittakerʹs functions are investigated in the paper. In particular, a class of these transformations involves the Lebedev index transformation with the square of the Macdonald function. Boundedness and inversion properties are derived in the weighted L2-spaces. The methods of Plancherelʹs theorems and Parsevalʹs equalities for the Fourier, Mellin and Kontorovich–Lebedev transforms are applied.