Abstract
We introduce the notion of bounded variation in the sense ofL 1-norm for periodic functions and prove a version of the classical Dirichlet-Jordan test for the convergence of Fourier series inL 1-norm. We also give an estimate of the rate of convergence.
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This research was started while the first named author visited Aligarh Muslim University during the spring semester of 1993. The author acknowledges the kind hospitality received there as well as the support by the Hungarian National Foundation for Scientific Research under Grant #016393.
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Móricz, F., Siddiqi, A.H. A quantified version of the Dirichlet-Jordan test inL 1-norm. Rend. Circ. Mat. Palermo 45, 19–24 (1996). https://doi.org/10.1007/BF02845086
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DOI: https://doi.org/10.1007/BF02845086