Title

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

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 Lp(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.

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