Titchmarsh Theorem by Modulus of Continuity for the Deformed Hankel–Lipschitz Classes

We give an analogue of the Titchmarsh theorem by modulus of continuity for the deformed Hankel-Lipschitz classes involving a deformed Hankel translation operator and equivalently described by the growth of the norm of the deformed Hankel transform for functions in \(L^{p}(\mathbb {R},|x|{ }^{2\alpha -1}dx)\) \((\alpha >1/4,1\leqslant p\leqslant 2).\)