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In this paper we study the so-called Radon inversion problem in bounded, circular, strictly convex domains with    $${\mathcal {C}}^2$$  C 2 boundary. We show that given    $$p&gt;0$$  p &gt; 0 and a strictly positive, continuous function    $$\Phi $$  Φ on    $$\partial \Omega $$  ∂ Ω , by use of homogeneous polynomials it is possible to construct a holomorphic function    $$f \in {\mathcal {O}}(\Omega )$$  f ∈ O ( Ω ) such that    $$\displaystyle \smallint _0^1 |f(zt)|^pdt = \Phi (z)$$  ∫ 0 1 | f ( z t ) | p d t = Φ ( z ) for all    $$z \in \partial \Omega $$  z ∈ ∂ Ω . 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.

Radon Inversion Problem for Holomorphic Functions on Circular, Strictly Convex Domains