Convergence of the Imaginary Parts of Simplest Fractions in L p(ℝ) for p < 1

Abstract

© 2014, Springer Science+Business Media New York. For p ∈ (1/2, 1), the Lp(ℝ)-convergence of the series (formula presented) are some points on the complex plane. The problem is solved completely in the case where the sequence {Re zk} has no limit points. The case where this sequence has finitely many limit points is also studied.