Hausdorff type operators and wavelet transform associated with the multidimensional Fourier-Bessel transform

Abstract

In the present paper, we introduce the Hausdorff operators associated with poly-axially operator $\Delta_{\alpha}$; and we prove the boundedness of the multidimensional Hankel-Hausdorff operators in space $L^2_{\alpha}(\mathbb{R}^d_+)$. We investigate multidimensional Hankel wavelet transform, and obtain some useful results. The relation between multidimensional Hankel wavelet transform and multidimensional Hankel-Hausdorff operators is also established. The properties of the adjoint multidimensional Hankel-Hausdorff operators are discussed. The results of this paper are illustrated by some examples, numerical tables, and figures.