Dual Boas type and weighted integrability results for deformed Hankel transform

We prove a dual Boas type result about connection between the integral behavior of a function in infinity and a generalized uniform smoothness of its deformed Hankel transform with parameter \(\kappa \ge \kappa _0\) $\kappa \ge {\kappa }_0$ , where \(k_0\) $k_0$ is the special constant from (1/4, 1/2). Also we give the conditions of weighted integrability for such transforms of functions from generalized integral Hölder-Lipschitz classes that extend previous ones by Elgargati, Loualid and Daher and Kumar, Restrepo and Ruzhansky. A Titchmarsh equivalence type theorem in corresponding \(L^2\) $L^2$ space is proved for deformed Hankel transform.