General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Izv. RAN. Ser. Mat.:

Personal entry:
Save password
Forgotten password?

Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 5, Pages 971–1003 (Mi izv1743)  

This article is cited in 25 scientific papers (total in 27 papers)

Trigonometric integrals

G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov

Abstract: A number of theorems on bounds, some sharp, are obtained for trigonometric integrals, and estimates which can be applied to investigations of singular integrals in the Tarry problem and its generalizations are derived.
Bibliography: 20 titles.

Full text: PDF file (2268 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1980, 15:2, 211–239

Bibliographic databases:

UDC: 511
MSC: Primary 10G10; Secondary 10J06
Received: 05.06.1978

Citation: G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Trigonometric integrals”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 971–1003; Math. USSR-Izv., 15:2 (1980), 211–239

Citation in format AMSBIB
\by G.~I.~Arkhipov, A.~A.~Karatsuba, V.~N.~Chubarikov
\paper Trigonometric integrals
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 5
\pages 971--1003
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 2
\pages 211--239

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Special cases of the theory of multiple trigonometric sums”, Math. USSR-Izv., 23:1 (1984), 17–82  mathnet  crossref  mathscinet  zmath
    2. G. I. Arkhipov, “On he Hilbert–Kamke problem”, Math. USSR-Izv., 24:1 (1985), 1–47  mathnet  crossref  mathscinet  zmath
    3. I. A. Ikromov, “Invariant estimates of two-dimensional trigonometric integrals”, Math. USSR-Sb., 67:2 (1990), 473–488  mathnet  crossref  mathscinet  zmath  isi
    4. D. A. Popov, “Estimates with constants for some classes of oscillatory integrals”, Russian Math. Surveys, 52:1 (1997), 73–145  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. D. A. Popov, “Reconstruction of characteristic functions in two-dimensional Radon tomography”, Russian Math. Surveys, 53:1 (1998), 109–193  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. G. I. Arkhipov, V. I. Blagodatskikh, V. S. Vladimirov, S. M. Voronin, O. B. Lupanov, E. F. Mishchenko, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, “Anatolii Alekseevich Karatsuba (on his 60th birthday)”, Russian Math. Surveys, 53:2 (1998), 419–422  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. M. A. Chahkiev, “On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem”, Izv. Math., 67:2 (2003), 405–418  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. I. A. Ikromov, “Damped Oscillatory Integrals and Maximal Operators”, Math. Notes, 78:6 (2005), 773–790  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. M. A. Chahkiev, “Estimates for oscillatory integrals with convex phase”, Izv. Math., 70:1 (2006), 171–209  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. D. A. Popov, “Remarks on uniform combined estimates of oscillatory integrals with simple singularities”, Izv. Math., 72:4 (2008), 793–816  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. I. A. Ikromov, “Summability of Oscillatory Integrals over Parameters and the Boundedness Problem for Fourier Transforms on Curves”, Math. Notes, 87:5 (2010), 700–719  mathnet  crossref  crossref  mathscinet  isi  elib
    12. I. Sh. Dzhabarov, “Ob otsenkakh trigonometricheskikh integralov”, Chebyshevskii sb., 11:1 (2010), 85–108  mathnet  mathscinet
    13. V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263  mathnet  mathscinet
    14. Willem L. Fouché, Safari Mukeru, “On the Fourier structure of the zero set of fractional Brownian motion”, Statistics & Probability Letters, 2012  crossref
    15. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  mathnet  crossref  crossref  zmath  isi  elib
    16. I. Sh. Dzhabbarov, “O pokazatele skhodimosti osobogo integrala mnogomernoi problemy Terri”, Chebyshevskii sb., 14:2 (2013), 74–103  mathnet
    17. V. N. Chubarikov, “Arifmeticheskie summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 16:2 (2015), 231–253  mathnet  elib
    18. I. A. Ikromov, “Integrability of the Fourier Transforms of Measures Concentrated on Hypersurfaces”, Funct. Anal. Appl., 49:3 (2015), 218–221  mathnet  crossref  crossref  isi  elib
    19. O. V. Kolpakova, V. N. Chubarikov, “Lineinye summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 17:1 (2016), 130–139  mathnet  elib
    20. A. R. Safarov, “Invariant Estimates of Two-Dimensional Oscillatory Integrals”, Math. Notes, 104:2 (2018), 293–302  mathnet  crossref  crossref  mathscinet  isi  elib
    21. I. A. Ikromov, Sh. A. Muranov, “Estimates of Oscillatory Integrals with a Damping Factor”, Math. Notes, 104:2 (2018), 218–230  mathnet  crossref  crossref  mathscinet  isi  elib
    22. I. A. Ikromov, S. E. Usmanov, “Ob ogranichennosti maksimalnykh operatorov, svyazannykh s giperpoverkhnostyami”, Sovremennye problemy matematiki i fiziki, SMFN, 64, no. 4, Rossiiskii universitet druzhby narodov, M., 2018, 650–681  mathnet  crossref
    23. I. Sh. Jabbarov, “Convergence Exponent of a Special Integral in the Two-Dimensional Tarry Problem with Homogeneous Polynomial of Degree 2”, Math. Notes, 105:3 (2019), 359–365  mathnet  crossref  crossref  mathscinet  isi  elib
    24. Sh. A. Muranov, “On estimates for oscillatory integrals with phase depending on parameters”, Ufa Math. J., 11:4 (2019), 78–90  mathnet  crossref  isi
    25. I. Sh. Dzhabbarov, “On the Multidimensional Tarry Problem for a Cubic Polynomial”, Math. Notes, 107:5 (2020), 713–726  mathnet  crossref  crossref  mathscinet  isi  elib
    26. Nigina A. Soleeva, “$L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities”, Zhurn. SFU. Ser. Matem. i fiz., 13:3 (2020), 350–359  mathnet  crossref
    27. M. A. Chahkiev, “Exact value of the exponent of convergence of the singular integral in Tarry's problem for homogeneous polynomials of degree $n$ in two variables”, Izv. Math., 85:2 (2021), 332–340  mathnet  crossref  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:919
    Full text:295
    First page:4

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021