Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$

Abstract

In this paper, we prove a generalization of Titchmarsh's theorem for the Laplace-Bessel differential operator in the space $L_{p,\gamma}(\mathbb{R}^{n}_{+})$ for functions satisfying the $(\psi,p)$-Laplace-Bessel Lipschitz condition for $1

0 $.

Keywords

• Laplace-Bessel differential operator,generalized shift operator,Laplace-Bessel Lipschitz function

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