One-Dimensional Fourier Series

Ferenc Weisz ()
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Ferenc Weisz: Eötvös Loránd University, Department of Numerical Analysis

Chapter Chapter 1 in Lebesgue Points and Summability of Higher Dimensional Fourier Series, 2021, pp 1-31 from Springer

Abstract: Abstract In this chapter, we present some theorems for one-dimensional Fourier series and for the Hardy-Littlewood maximal function. In Sect. 1.1, we introduce the $$L_p({\mathbb T})$$ L p ( T ) spaces and prove some basic inequalities. In Sect. 1.2, we prove that the partial sums of the Fourier series are uniformly bounded on the $$L_p({\mathbb T})$$ L p ( T ) spaces when $$1

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-74636-0_1

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DOI: 10.1007/978-3-030-74636-0_1

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