Abstract
We establish the Hausdorff–Young type theorem in L p (R +), 1 ≤ p ≤ 2, which gives the norm estimates and an inversion formula for the Lebedev integral with respect to an index of the Macdonald function. The case p = 2 is known as the Plancherel theorem for the modified Kontorovich–Lebedev transform.
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