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The problem of weighted integrability of the Fourier–Laguerre transform in terms of the moduli of smoothness related to generalized translations is considered. Sufficient conditions are given to solve this problem. These results generalize a famous Titchmarsh's theorem and Younis' theorem, due to Negzaoui in the Laguerre hypergroup. Also some results connected with the integrability of Fourier–Laguerre transforms of Laguerre convolutions are given.

Sufficient conditions for the weighted integrability of Fourier–Laguerre transforms