A very general asymptotic type formula is presented for the Lebesgue constants of both Fourier partial sums and linear methods of summability of Fourier series in the multivariate Euclidean spaces. More precisely, the obtained formula represents the norm of a trigonometric polynomial with coefficients being the values of a multiplier as the norm of the Fourier transform of this multiplier, with an error which in many cases (after appropriate estimates) leads either to a really asymptotic relation or to a suitable upper estimate.
|Number of pages||8|
|Journal||Journal of Mathematical Sciences|
|State||Published - Dec 2022|
Bibliographical noteFunding Information:
This work is financially supported and performed under the auspices of the Iran National Science Foundation and the University of Tarbiat Modares in the program of postdoctoral research projects.
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