ABSTRACT

Hankel-$K\left\{M_p\right\}$ spaces, as introduced by the second-named author, play the same role in the theory of the Hankel transformation as the Gelfand-Shilov $K\left\{M_p\right\}$ spaces in the theory of the Fourier transformation. For $\mu >-1/2$, under suitable restrictions on the weights $\{M_p{\}}_{p=0}^{\mathrm{\infty }}$, the topology of a Hankel-$K\left\{M_p\right\}$ space E can be generated by norms of $L^q$-type $(1\le q\le \mathrm{\infty })$ involving the Bessel operator $S_{\mu }$. In this paper, adapting a technique due to Kamiński, the elements of the dual space $E^{\prime }$ are represented as $S_{\mu }$-distributional derivatives of a single continuous function. Corresponding characterizations of boundedness and convergence in (the weak, weak*, strong topologies of) $E^{\prime }$ are obtained.

摘要

汉高$ķ\left\{{\mathrm{中号}}_p\right\}$ 正如第二名作者所介绍的那样，空间在汉克尔变换理论中扮演的角色与杰芬德·希洛夫（Gelfand-Shilov）相同。 $ķ\left\{{\mathrm{中号}}_p\right\}$傅立叶变换理论中的空间。为了$\mu >-\mathrm{1个}/\mathrm{2个}$，在适当的重量限制下 $\{{\mathrm{中号}}_p{\}}_{p=0}^{\mathrm{\infty }}$，汉克尔的拓扑结构$ķ\left\{{\mathrm{中号}}_p\right\}$可以通过以下范数来生成空间E${\mathrm{大号}}^q$-类型 $（\mathrm{1个}\le q\le \mathrm{\infty }）$ 涉及贝塞尔算子 ${\mathrm{小号}}_{\mu }$。在本文中，由于双重空间的元素Kamiński而采用了一种技术$E^{\prime }$ 表示为 ${\mathrm{小号}}_{\mu }$-单个连续函数的分布导数。（的弱，弱*，强拓扑）中有界和收敛的相应特征$E^{\prime }$ 获得。