We deal with a class of one-parameter family of integral transforms of Bargmann type arising as dual transform of fractional Hankel transform. Their ranges are identified to be special subspaces of the weighted hyperholomorphic left Hilbert spaces, generalizing the slice Bergman space of the second kind. Their reproducing kernel is given by closed expression involving the ⋆-regularization of Gauss hypergeometric function. We also discuss their basic properties such as boundedness and we determine their singular values. Moreover, we describe their compactness and membership in p-Schatten classes. The operational calculus for this transform is also investigated.

我们处理作为分数汉克尔变换的对偶变换而产生的一类巴格曼型积分变换的单参数族。它们的范围被确定为加权超全纯左希尔伯特空间的特殊子空间，概括了第二类切片伯格曼空间。它们的再生核由涉及高斯超几何函数的⋆正则化的封闭表达式给出。我们还讨论了它们的基本属性，例如有界性，并确定了它们的奇异值。此外，我们描述了它们在p -Schatten 类中的紧凑性和成员资格。还研究了这种变换的运算演算。