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

Alexander M. Stokolos, Walter Trebels

Research output: Contribution to book or proceedingConference articlepeer-review

1 Scopus citations

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 tμ, 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.

Original languageEnglish
Title of host publicationRecent Advances in Harmonic Analysis and Applications
Subtitle of host publicationIn Honor of Konstantin Oskolkov
PublisherSpringer New York LLC
Pages339-355
Number of pages17
ISBN (Print)9781461445647
DOIs
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume25
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Fingerprint

Dive into the research topics of 'Moduli of Smoothness and Rate of a.e. Convergence for Some Convolution Operators'. Together they form a unique fingerprint.

Cite this