N-dimensional Hankel transform and complex powers of Bessel operator

In this paper, we study a version of the n-dimensional Hankel transform on certain spaces ℋμ which were studied in [Molina, S., 2003, A generalization of the spaces ℋμ and and the space of multipliers. Actas del VII Congreso Dr. Antonio Monteiro, pp. 49–56.]. Moreover, we introduce an n-dimensional generalization of Bessel operator and we have studied its properties in relation to the Hankel transform. Moreover, we study some application to the study of the fractional powers of Bessel operator on L2 (Rn+). Fil: Trione, Susana Elena. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina