Abstract:
In the paper, we consider the $q$-integrability of functions $\lambda(t)|\mathcal F_{q, \nu}(f)(t)|^r$, where $\lambda(t)$ is a Gogoladze-Meskhia-Moricz type weight and $\mathcal F_{q, \nu}(f)(t)$ is the $q$-Bessel Fourier transforms of a function $f$ from generalized integral Lipschitz classes. There are some corollaries for power type and constant weights, which are analogues of classical results of Titchmarsh et al. Also, a $q$-analogue of the famous Herz theorem is proved.
Keywords:$q$-Bessel Fourier transform, $q$-Bessel translation, modulus of smoothness, weights of Gogoladze–Meskhia type, $q$-Besov space.
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