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

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http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/653 http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/653 http://eprints.org/relation/isIndexCodesVersionOf http://etheses.bham.ac.uk/id/document/653 archive 4031 disk0/00/00/02/68 2009-09-30 13:19:20 2019-01-23 09:51:49 2011-07-19 16:14:58 thesis show 0 Bailey Andrew David baileya@for.mat.bham.ac.uk Bennett Jon University of Birmingham Almost everywhere convergence of dyadic partial sums of Fourier series for almost periodic functions unpub QA 10col_ephy Almost Periodic Functions, Fourier Series, Convergence, Maximal Operator, Stepanov Space, Fourier Summation, Littlewood-Paley Theory, Hilbert Transform The addendum file dates from October 2010. 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operator bounds and convergence issues in Stepanov spaces. 2009-07 2008-09 graduation 2853183 eng author unchecked This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public 81 University of Birmingham School of Mathematics m_ph FALSE na 2009-07 graduation