Almost everywhere convergence of dyadic partial sums of Fourier series for almost periodic functions

It is a classical result that for a function \(f\) \(\in\) L^p(\(\char{bbold10}{0x54}\)), dyadic partial sums of the Fourier series of \(f\) converge almost everywhere for \(p\) \(\in\) (1, \(\infty\)). In 1968, E. A. Bredihina established an analogous result for the Stepanov spaces of almost periodic functions in the case \(p\) = 2. Here, a new proof of the almost everywhere convergence result for Stepanov spaces is presented by way of a bound on an appropriate maximal operator for \(p\) = 2^k, \(k\) \(\in\) \(\char{bbold10}{0x4E}\). In the process of establishing this, a number of general results are obtained that will facilitate further work pertaining to operator bounds and convergence issues in Stepanov spaces.

Name dc:type.qualificationname

m_ph

Level dc:type.qualificationlevel

m_ph

Grantor dc:publisher.institution

University of Birmingham

Year dc:date.issued

2009

Author dc:creator

• Bailey, Andrew David

• QA Mathematics

Repository record dc:identifier.uri

http://etheses.bham.ac.uk//id/eprint/268/2/Decl_IS_Bailey09MPhil.jpg

OAI identifier oai:identifier

oai:etheses.bham.ac.uk:268