Boundedness of the Pseudo-differential Bessel Operators on Sobolev and Bessel Potential Spaces

An \(n\) -dimensional pseudo-differential Bessel operators \({\mathcal{B}}_{\alpha,a}\) involving the multidimensional Fourier–Bessel transformation is defined. Then, we introduce some class of symbols and we prove that \({\mathcal{B}}_{\alpha,a}\) are bounded on Sobolev and Bessel potentials spaces. Moreover, a generalized Bessel potential is defined and its properties are investigated.