Estimation of Dirichlet kernel difference in the norm of L / V. O. Tonkov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 12-18 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 10-15].

This work is related to the problem of estimation of the norm of a trigonometrical polynomials through their coefficient in L. It is proved that the norm of the difference of Dirichlet's kernels in L has the precise order \ln(n-m) and the lower estimate is also valid with the coefficient 4/\pi^{2}. A theorem and two lemmas are presented showing that the coefficients c at \ln(n-m) in an asymptotc estimate uniform with resepect to m and n may be greater than 4/\pi^{2} and its value in examples depends on arithmetic properties of n and m.

Key words: norm of a trigonometrical polynomial in L, asymptotic estimate.

№ 1/2010