The paper deals with the k-plane transform \({\mathcal {R}}_{k}\) on the Heisenberg group. We study the properties of the transform \({\mathcal {R}}_{k}\) and obtain three types of inversion formulas for \({\mathcal {R}}_{k}\). The first inversion is deduced with the help of the group Fourier transform, together with the partial Riesz potential and Heisenberg sublaplacian. By this formula, another two formulas are established in terms with the adjoint of \({\mathcal {R}}_{k}\) and the wavelet, respectively.

中文翻译：

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海森堡群上的k平面变换

本文处理了Heisenberg组的k平面变换\（{\ mathcal {R}} _ {k} \）。我们研究的变换特性\（{\ mathcal {R}} _ {K} \） ，将获得三种类型的反演公式为\（{\ mathcal {R}} _ {K} \） 。首次反演是借助傅立叶变换，部分Riesz势和Heisenberg次拉普拉斯推论得出的。通过该公式，分别根据\（{\ mathcal {R}} _ {k} \）和小波的伴随关系建立了另外两个公式。