We prove the analogue of Hörmander-Mikhlin multiplier theorem for the multidimensional Fourier-Bessel transform associated with the Poly-axially operator.

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An n-dimensional pseudo-differential Bessel operators Bα,a involving the multidimensional Fourier-Bessel transformation is defined. Then, we introduce some class of symbols and we prove that Bα,a are bounded on Sobolev and Bessel potentials spaces. Moreover, a generalized Bessel potential is defined and its properties are investigated.

No abstract