Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators

Authors

Alexander M. Stokolos, Georgia Southern UniversityFollow
Walter Trebels, TU Darmstadt

Document Type

Conference Proceeding

Publication Date

2013

Publication Title

Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov

DOI

10.1007/978-1-4614-4565-4_27

ISBN

978-1-4614-4565-4

Abstract

One purpose of this chapter is to establish results on the rate of almost everywhere convergence of approximation processes of convolution type in L^p(Rⁿ),where instead of a particular rate (like t ^μ, μ > 0, t → 0+), fractional moduli of smoothness are employed. An essential tool is a modified K-functional. Away from saturation orders these results are nearly optimal. A second purpose is to illustrate that the methods applied also work in other settings which feature a convolution/multiplier structure.

Recommended Citation

Stokolos, Alexander M., Walter Trebels. 2013. "Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators." Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov, Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, and Brett D. Wick (Ed.), 25: 339-355 New York, NY: Springer. doi: 10.1007/978-1-4614-4565-4_27 isbn: 978-1-4614-4565-4
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/188