The Gibbs phenomenon for Riesz spherical means of multiple Fourier series was discovered and the Gibbs constants for these means from below were estimated. The necessary and sufficient conditions for convergence in Pringsheim sense of multiple Fourier series of functions of bounded $\Phi$-variation of Hardy type were obtained. The boundedness of the Hardy operator in real Hardy spaces $H(R)$ and $H(T)$ was proved. The similar result for dyadic Hardy operator was also obtained. The analogue of tauberian theorem of Wiener in dyadic harmonic analysis was proved. As a corollary the following two criteria were obtained: 1) the linear hull of the set $\{f(\cdot\oplus y):y\ge0\}$ of dyadic shifts of a given function $f\in L(\mathbb{R}_+)$ is dens in the space $L(\mathbb{R}_+)$ iff the Walsh–Fourier transform $\tilde f(x)$ is not equal to zero on positive half-line $\mathbb{R}_+$ (dyadic analogue of the criterion of Wiener); 2) in order the linear hull of the set $\{f(\cdot\oplus y):0\le y<1\}$ of all dyadic shifts of the given function $f\in L[0,1)$ be dens in the space $L[0,1)$, it is necessary and sufficient that all Walsh–Fourier coefficients of the function $f\in L[0,1)$ are not equal to zero.

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1961 (department of theory of functions and functional analysis). Ph.D. thesis was defended in 1964. D.Sci. thesis was defended in 1975. A list of my works contains more than 80 titles. I am the member of Organizing Committees of Saratov Winter Schools on Function Theory (since 1988), Voronezh Winter Schools on Function Theory (since 1993) and Kazan Summer Schools on Function Theory (since 1995).

• B. I. Golubov, A. V. Efimov, V. A. Skvortsov. Ryady i preobrazovaniya Uolsha. Teoriya i primeneniya. M.: Nauka, 1987. (B. Golubov, A. Efimov, V. Skvortsov. Walsh series and transforms. Theory and applications. Kluver Academic Publishers, Dordrecht, Boston, London, 1991).
• B. I. Golubov. Elementy dvoichnogo analiza. M.: MGUP, 2005.
• B. I. Golubov. Ogranichennost operatorov Khardi i Khardi–Littlvuda v prostranstvakh Re H i BMO // Matem. sb., t. 188, # 7 (1997), 93–106.
• B. I. Golubov. Ob analoge neravenstva Khardi dlya preobrazovaniya Fure–Uolsha // Izv. RAN. Ser. matem., t. 65, # 3 (2001), 3–14.
• B. I. Golubov. Dvoichnyi analog tauberovoi teoremy Vinera i smezhnye voprosy // Izv. RAN. Ser. matem., t. 67, # 1, (2003), 33–58.
• B. I. Golubov. O modifitsirovannom silnom dvoichnom integrale i proizvodnoi // Matem. sb., t. 193, # 4 (2002), 37–60.

• Moscow Institute of Physics and Technology (State University)
• Moscow Mathematical Society
• Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region