In the present paper, we introduce the Hausdorff operators associated with the multidimensional Fourier-Bessel operator ∆α; and we prove the boundedness of the multidimensional Fourier-Bessel-Hausdorff operators on the space L_α² (R_+ᵈ). We investigate multidimensional Fourier-Bessel wavelet transform, and obtain some useful results. The relation between the multidimensional Fourier-Bessel wavelet transform and multidimensional Fourier-Bessel-Hausdorff operators is also established. The properties of the adjoint multidimensional Fourier-Bessel-Hausdorff operators are further discussed. The results of this paper are illustrated by some examples and figures.
Soltani et al. (Wed,) studied this question.