On Fourier–Haar coefficients of the function from the Marcinkiewicz space |
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| Authors: | Alexandr Usachev |
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| Institution: | School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia |
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| Abstract: | The main objective of the paper is to describe asymptotic behaviour of Fourier–Haar coefficients of functions from Marcinkiewicz spaces. We also discuss the Cesàro summability and the almost convergence of sequences related to Fourier–Haar coefficients and generalise a result from 17]. Some analogues of Mercer's theorem for Fourier coefficients are proved. |
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| Keywords: | Haar system Fourier coefficients Marcinkiewicz spaces Almost convergence Mercer's theorem |
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