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Vol 76, No 6 (2021)
Functions with general monotone Fourier coefficients
Abstract
This paper is a study of trigonometric series with general monotone coefficients in the class $\operatorname{GM}(p)$ with $p\geqslant 1$. Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For $1 < p < \infty$ two-sided estimates are obtained for the $L_p$-moduli of smoothness of sums of series with $\operatorname{GM}(p)$-coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients.
Bibliography: 99 titles.
Uspekhi Matematicheskikh Nauk. 2021;76(6):3-70
3-70
71-118
Non-commutative methods in additive combinatorics and number theory
Abstract
The survey is devoted to applications of growth in non-Abelian groups to a number of problems in number theory and additive combinatorics. We discuss Zaremba's conjecture, sum-product theory, incidence geometry, the affine sieve, and some other questions.Bibliography: 149 titles.
Uspekhi Matematicheskikh Nauk. 2021;76(6):119-180
119-180
Èrnest Borisovich Vinberg (obituary)
Uspekhi Matematicheskikh Nauk. 2021;76(6):181-192
181-192
Local groups in Delone sets: a conjecture and results
Uspekhi Matematicheskikh Nauk. 2021;76(6):193-194
193-194
On compatible diagonal metrics
Uspekhi Matematicheskikh Nauk. 2021;76(6):195-196
195-196
3-manifolds represented by 4-regular graphs with three Eulerian cycles
Uspekhi Matematicheskikh Nauk. 2021;76(6):197-198
197-198
Twisted tensor products of DG algebras
Uspekhi Matematicheskikh Nauk. 2021;76(6):199-200
199-200
Vladimir Igorevich Bogachev (on his 60th birthday)
Uspekhi Matematicheskikh Nauk. 2021;76(6):201-208
201-208