Abstract. In 2003, F. Móricz proved that the jumps of a periodic function at its simple discontinuities can be determined by its conjugate Abel--Poisson mean. Later Q. L. Shi and X. L. Shi introduced the concentration factors method of Abel--Poisson type and established a criterion for functions that satisfied a condition of Dini type. For piecewise smooth functions the convergence rate of this method is usually faster then Móricz Process. In this paper we establish a new criterion for concentration factors without the condition of Dini type.

AMS Subject Classification (1991): 42A50, 42A16

Keyword(s): jump, Abel--Poisson concentration factors, convergence rate

Received July 12, 2008, and in revised form August 30, 2010. (Registered under 74/2010.)