On the injectivity of the Pompeiu transform for integral ball means - Ochakovskaya, O. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
An uniqueness theorem is proved for functions in $\mathbb{R}^n, n ≥ 2$, with vanishing integrals over balls of fixed radius and a given majorant of growth. The problem of the unimprovability of this theorem is considered.