On distributional point values and boundary values of analytic functions
We give the following version of Fatou's theorem for distributions that are boundary values of analytic functions. We prove that if f D′ (a, b) is the distributional limit of the analytic function F defined in a region of the form (a,b) × (0,R), if the one sided distributional limit exists. F (*0 + 0) = γ and if f is distributionally bounded at x = x0, then the Lojasiewicz point value exists, f(x0) = γ distributionally, and in particular F(z)→ γ as z → x0 in a non-tangential fashion.
Publication Source (Journal or Book title)
Rendiconti del Seminario Matematico
Estrada, R., & Vindas, J. (2012). On distributional point values and boundary values of analytic functions. Rendiconti del Seminario Matematico, 70 (2), 121-126. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/289