On Representation, Boundedness and Convergence of Hankel-K{Mp}' Generalized Functions

Abstract

Under opportune assumptions on the defining sequence $\{M_p{\}}_{p=0}^{\infty }$, Hankel-$K\{M_p{\}}^{\prime }$ generalized functions can be represented as

where $k\in \mathbb{N}$ and $F$ is a continuous function on $I=(0,\infty )$ such that $M_r^{-1}F\in L^q(I)$ $(1\le q\le \infty )$ for some $r\in \mathbb{N}$. A corresponding characterization of boundedness and convergence of Hankel-$K\{M_p{\}}^{\prime }$ generalized functions is given.