Approximation of Functions by Singular Integrals

Rahim M. Rzaev; Gulnara Kh. Mammadova; Mansur Sh. Maharramov

doi:doi:10.11648/j.pamj.20140306.11

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Approximation of Functions by Singular Integrals

Rahim M. Rzaev, Gulnara Kh. Mammadova, Mansur Sh. Maharramov

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6)

Received: 2 November 2014 Accepted: 13 November 2014 Published: 17 November 2014

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Abstract

In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 6)
DOI	10.11648/j.pamj.20140306.11
Page(s)	113-120
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Approximation, Singular Integrals, Bounded Mean Oscillation, Vanishing Mean Oscillation

References

[1]	Butzer P.L., Nessel R.J. Fourier analysis and approximation. Vol.1: One-Dimensional Theory. New York and London, 1971.
[2]	Calderon A.P., Zygmund A. On the existence of certain singular integrals. Acta. Math., 1952, v.88, pp.85-139.
[3]	Gadzhiev N.M., Rzaev R.M. On the order of locally summable functions approximation by singular integrals. Funct. Approx. Comment. Math., 1992, v.20, pp.35-40.
[4]	Garnett J.B. Bounded analytic functions. Academic Press Inc., New York, 1981.
[5]	Golubov B.I. On asymptotics of multiple singular integrals for differentiable functions. Matem. Zametki, 1981, v.30, No5, pp.749-762 (Russian).
[6]	Janson S. On functions with conditions on the mean oscillation. Ark. math., 1976, v.14, No2, pp. 189-196.
[7]	John F., Nirenberg L. On functions of bounded mean oscillation. Comm. Pure Appl. Math., 1961, v.14, pp.415-426.
[8]	Kerman R.A. Pointwise convergent approximate identities of dilated radially decreasing kernels. Proc. Amer. Math. Soc., 1987, v.101, No1, pp.41-44.
[9]	Rzaev R.M. On approximation of essentially continuous functions by singular integrals. Izv. Vuzov. Matematika, 1989, No3, pp.57-62 (Russian).
[10]	Rzaev R.M. On approximation of locally summable functions by singular integrals in terms of mean oscillation and some applications. Preprint Inst. Phys. Natl. Acad. Sci. Azerb., 1992, №1, p.1-43 (Russian).
[11]	Rzaev R.M. A multidimensional singular integral operator in the spaces defined by conditions on the -th order mean oscillation. Dokady Mathematics, 1997, v.56, No2, pp.747-749.
[12]	Rzaev R.M., Aliyeva L.R. On local properties of functions and singular integrals in terms of the mean oscillation. Cent. Eur. J. Math., 2008, v.6, No4, p.595-609.
[13]	Sarason D. Functions of vanishing mean oscillation. Trans. Amer. Math. Soc., 1975, v.207, pp. 391-405.
[14]	Spanne S. Some function spaces defined using the mean oscillation over cubes. Ann. Scuola Norm. Sup. Pisa, 1965, v.19, No4, pp.593-608.
[15]	Stein E.M., Singular integrals and differentiability properties of functions. Princeton University Press. Princeton, New J., 1970.
[16]	Stein E.M., Weiss G. Introduction to Fourier Analysis on Euclidean spaces. Princeton University Press. Princeton, New J., 1971.

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Rahim M. Rzaev, Gulnara Kh. Mammadova, Mansur Sh. Maharramov. (2014). Approximation of Functions by Singular Integrals. Pure and Applied Mathematics Journal, 3(6), 113-120. https://doi.org/10.11648/j.pamj.20140306.11

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ACS Style

Rahim M. Rzaev; Gulnara Kh. Mammadova; Mansur Sh. Maharramov. Approximation of Functions by Singular Integrals. Pure Appl. Math. J. 2014, 3(6), 113-120. doi: 10.11648/j.pamj.20140306.11

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AMA Style

Rahim M. Rzaev, Gulnara Kh. Mammadova, Mansur Sh. Maharramov. Approximation of Functions by Singular Integrals. Pure Appl Math J. 2014;3(6):113-120. doi: 10.11648/j.pamj.20140306.11

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@article{10.11648/j.pamj.20140306.11,
  author = {Rahim M. Rzaev and Gulnara Kh. Mammadova and Mansur Sh. Maharramov},
  title = {Approximation of Functions by Singular Integrals},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6},
  pages = {113-120},
  doi = {10.11648/j.pamj.20140306.11},
  url = {https://doi.org/10.11648/j.pamj.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140306.11},
  abstract = {In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.},
 year = {2014}
}

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TY  - JOUR
T1  - Approximation of Functions by Singular Integrals
AU  - Rahim M. Rzaev
AU  - Gulnara Kh. Mammadova
AU  - Mansur Sh. Maharramov
Y1  - 2014/11/17
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140306.11
DO  - 10.11648/j.pamj.20140306.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 113
EP  - 120
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140306.11
AB  - In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.
VL  - 3
IS  - 6
ER  -

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Author Information

Rahim M. Rzaev

Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, AZ1141, Azerbaijan
Gulnara Kh. Mammadova

Department of Mathematics and Informatics of Ganja State University, Ganja, Azerbaijan
Mansur Sh. Maharramov

Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, AZ1141, Azerbaijan

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APA Style

Rahim M. Rzaev, Gulnara Kh. Mammadova, Mansur Sh. Maharramov. (2014). Approximation of Functions by Singular Integrals. Pure and Applied Mathematics Journal, 3(6), 113-120. https://doi.org/10.11648/j.pamj.20140306.11

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ACS Style

Rahim M. Rzaev; Gulnara Kh. Mammadova; Mansur Sh. Maharramov. Approximation of Functions by Singular Integrals. Pure Appl. Math. J. 2014, 3(6), 113-120. doi: 10.11648/j.pamj.20140306.11

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AMA Style

Rahim M. Rzaev, Gulnara Kh. Mammadova, Mansur Sh. Maharramov. Approximation of Functions by Singular Integrals. Pure Appl Math J. 2014;3(6):113-120. doi: 10.11648/j.pamj.20140306.11

Copy | Download

@article{10.11648/j.pamj.20140306.11,
  author = {Rahim M. Rzaev and Gulnara Kh. Mammadova and Mansur Sh. Maharramov},
  title = {Approximation of Functions by Singular Integrals},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {6},
  pages = {113-120},
  doi = {10.11648/j.pamj.20140306.11},
  url = {https://doi.org/10.11648/j.pamj.20140306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140306.11},
  abstract = {In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Approximation of Functions by Singular Integrals
AU  - Rahim M. Rzaev
AU  - Gulnara Kh. Mammadova
AU  - Mansur Sh. Maharramov
Y1  - 2014/11/17
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140306.11
DO  - 10.11648/j.pamj.20140306.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 113
EP  - 120
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140306.11
AB  - In this work questions on approximation of locally summable functions by singular integrals are investigated. Was estimated the rate of approximation in terms of various metric characteristics describing the structural properties of the given function.
VL  - 3
IS  - 6
ER  -

Copy | Download