Weighted Turán type inequality for rational functions with prescribed poles

摘要

Firstly, we introduce a new type of weight functions named as N-doubling weights, which is an essential generalization of the well known doubling weights. Secondly, we establish a weighted Tur′ an type inequality with N-doubling weights and a Nikolskii-Tur′ an type inequality for rational functions with prescribed poles. Our results generalize some known Tur ′ an type inequality both for polynomials and rational functions.