Interpolation of functions with zero spherical averages obeying growth constraints (Q6631333)

In this paper the authors study the following problem: let \(V_r({ \mathbb{R} }^n) \), with \(n\geq 2\) and \(r>0 \), be the set of locally integrable functions \(f:{ \mathbb{R} }^n\to{ \mathbb{C} }\) with the zero integrals over all balls of radius \(r\) in \({ \mathbb{R} }^n \). They study the interpolation problem \(f(a_k)=b_k \), with \(k=1,2,\dots \), for functions in \((V_r\cap C^{\infty})({ \mathbb{R} }^n)\) with growth constraints at infinity. Under proper conditions, this interpolation problem is shown to be solvable.