LAUSR

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.