A sharp estimate for the rate of convergence in mean of Birkhoff sums for some classes of periodic differentiable functions

Author: Rozhdestvenskii A.  

Publisher: Springer Publishing Company

ISSN: 0016-2663

Source: Functional Analysis and Its Applications, Vol.40, Iss.1, 2006-01, pp. : 34-41

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

For a badly approximable vector α, we obtain a sharp estimate for the rate of convergence in the space L p (0 < p < ∞) of the Birkhoff means for an absolutely continuous periodic function f and for functions in spaces of Bessel potentials.