Letter to the editor concerning the communication ``A Property of Fourier Series'' by A.\,M.~Rubinov

N. I. Chernykh

Matematičeskie zametki, Tome 8 (1970) no. 6, pp. 823-825.

Résumé

A. M. Rubinov [1], in his article published in our journal, used the powerful methods of functional and, in particular, harmonic analysis in the proof of his main result. All the results presented in this work except S. B. Stechkin's example are, however, simple consequences of Schwartz's lemma, which states that any function $f(z)$ regular in the disk $|z|\leqslant\delta$ such that $f(0)=0$ satisfies the inequality $|f(z)|\leqslant K|z|$, $K=K(\delta,f)$.