The Lebesgue Constants of Fourier Partial Sums
We give a brief overview of the results on the behavior of the Lebesgue constants for various partial sums of multiple Fourier series. In addition, we establish a new property of the Lebesgue constants concerning its partly increasing behavior.
KeywordsFourier series Partial sum Lebesgue constant Homothety
2010 Mathematics Subject ClassificationPrimary 42B15; Secondary 42B05 42A05
The authors acknowledge the support of the Gelbart Institute at the Mathematics Department in Bar-Ilan University.
The authors are indebted to the referee for thorough reading and valuable remarks and suggestions.
Last but not least, the authors thank A. Podkorytov for bringing their attention to Szegö’s result and for interesting discussions.
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