RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki

Mat. Zametki, 2016, Volume 99, Issue 4, Pages 502–510 (Mi mzm10844)

The Hardy–Littlewood Theorem for Multiple Fourier Series with Monotone Coefficients
M. I. Dyachenko, E. D. Nursultanov, M. E. Nursultanov

References

1. H. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961  mathscinet
2. F. Móricz, “On double cosine, sine and Walsh series with monotone coefficients”, Proc. Amer. Math. Soc., 109:2 (1990), 417–425  crossref  mathscinet  zmath
3. M. I. Dyachenko, “O skhodimosti dvoinykh trigonometricheskikh ryadov i ryadov Fure s monotonnymi koeffitsientami”, Matem. sb., 129:1 (1986), 55–72  mathnet  mathscinet  zmath
4. M. I. D'jachenko, “Multiple trigonometric series with lexicographically monotone coefficients”, Anal. Math., 16:3 (1990), 173–190  crossref  mathscinet  zmath
5. M. I. Dyachenko, “Normy yader Dirikhle i nekotorykh drugikh trigonometricheskikh polinomov v prostranstvakh $L_p$”, Matem. sb., 184:3 (1993), 3–20  mathnet  mathscinet  zmath
6. E. D. Nursultanov, “Setevye prostranstva i neravenstva tipa Khardi–Litlvuda”, Matem. sb., 189:3 (1998), 83–102  mathnet  crossref  mathscinet  zmath
7. E. D. Nursultanov, “Interpolation properties of some anisotropic spaces and Hardy–Littlewood type inequalities”, East J. Approx., 4:2 (1998), 243–275  mathscinet  zmath
8. M. Dyachenko, S. Tikhonov, “Convergence of trigonometric series with general monotone coefficients”, C. R. Math. Acad. Sci. Paris, 345:3 (2007), 123–126  crossref  mathscinet  zmath
9. M. Dyachenko, S. Tikhonov, “A Hardy–Littlewood theorem for multiple series”, J. Math. Anal. Appl., 339:1 (2008), 503–510  crossref  mathscinet  zmath
10. M. Dyachenko, S. Tikhonov, “Integrability and continuity of functions represented by trigonometric series: coefficients criteria”, Studia Math., 193:3 (2009), 285–306  crossref  mathscinet  zmath
11. V. A. Yudin, “Povedenie konstant Lebega”, Matem. zametki, 17:3 (1975), 401–405  mathnet  mathscinet  zmath
12. L. Colzani, P. M. Soardi, “$L^p$-norms of certain kernels of the $N$-dimensional torus”, Trans. Amer. Math. Soc., 266:2 (1981), 617–627  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2026