In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with \({\mathcal {C}}^2\) boundary. We show that given \(p>0\) and a strictly positive, continuous function \(\Phi \) on \(\partial \Omega \), by use of homogeneous polynomials it is possible to construct a holomorphic function \(f \in {\mathcal {O}}(\Omega )\) such that \(\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)\) for all \(z \in \partial \Omega \). In our approach we make use of so-called lacunary K-summing polynomials (see definition below) that allow us to construct solutions with in some sense extremal properties.

在本文中，我们研究了具有\({\mathcal {C}}^2\)边界的有界、圆形、严格凸域中的所谓氡反演问题。我们证明给定\(p>0\)和\(\partial \Omega \)上的严格正连续函数\(\Phi \)，通过使用齐次多项式可以构造全纯函数\(f \in {\mathcal {O}}(\Omega )\)使得\(\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)\)对于所有\(z \in \)部分 \Omega \)。在我们的方法中，我们利用所谓的缺失K- 求和多项式（见下面的定义），使我们能够构造具有某种意义上的极值特性的解。