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

### Abstract

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

Topics: QA Mathematics
Year: 2009
OAI identifier: oai:etheses.bham.ac.uk:268

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