On the uniform convergence of special sine integrals
The title more or less reflects the subject of the paper: certain conditions are obtained that ensure the uniform convergence of the sine Fourier integrals. There are two main problems with this paper: novelty of the obtained results and introduced definitions and references. In fact, these problems are closely related: if the references were not incomplete and sometimes misleading, many of the results would not be published (at least, in the present form) because they were earlier obtained in the paper by \textit{M. Dyachenko, E. Liflyand} and \textit{S. Tikhonov} [J. Math. Anal. Appl. 372, 328--338 (2010; Zbl 1201.42003)]. In addition, the author claims that he generalizes his own results on trigonometric series from [Acta Math. Hungar. 128, 369--380 (2010; Zbl 1240.42015)] but in fact the paper by \textit{M. Dyachenko} and \textit{S. Tikhonov} [Stud. Math. 193, 285--306 (2009; Zbl 1169.42001)] should be mentioned as a real prototype. Not less important are the used classes of functions. As for the preceding analogs for sequences, they should be attributed to S. Tikhonov; the best reference here is the recent survey paper, both on sequences and functions, by \textit{E. Liflyand} and \textit{S. Tikhonov}, [Math. Nachr. 284, 1083--1098 (2011; Zbl 1223.26017)].
scientific article; zbMATH DE number 5990914