On local properties of functions and singular integrals in terms of the mean oscillation

Rahim Rzaev; Lala Aliyeva

Open Mathematics (2008)

  • Volume: 6, Issue: 4, page 595-609
  • ISSN: 2391-5455

Abstract

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This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.

How to cite

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Rahim Rzaev, and Lala Aliyeva. "On local properties of functions and singular integrals in terms of the mean oscillation." Open Mathematics 6.4 (2008): 595-609. <http://eudml.org/doc/268973>.

@article{RahimRzaev2008,
abstract = {This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.},
author = {Rahim Rzaev, Lala Aliyeva},
journal = {Open Mathematics},
keywords = {mean oscillation; local properties of functions; singular integrals},
language = {eng},
number = {4},
pages = {595-609},
title = {On local properties of functions and singular integrals in terms of the mean oscillation},
url = {http://eudml.org/doc/268973},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Rahim Rzaev
AU - Lala Aliyeva
TI - On local properties of functions and singular integrals in terms of the mean oscillation
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 595
EP - 609
AB - This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.
LA - eng
KW - mean oscillation; local properties of functions; singular integrals
UR - http://eudml.org/doc/268973
ER -

References

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  1. [1] Bari N.K., Stechkin S.B., Best approximation and differentiability properties of two conjugate functions, Tr. Mosk. Mat. Obs., 1956, 5, 483–522 (in Russian) 
  2. [2] Calderon A.P., Zygmund A., Local properties of solutions of elliptic partial differential equations, Studia Math., 1961, 20, 171–225 Zbl0099.30103
  3. [3] DeVore R., Sharpley R., Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 1984, 47, 1–115 Zbl0529.42005
  4. [4] Nakai E., On the restriction of functions of bounded mean oscillation to the lower dimensional space, Arch. Math. (Basel), 1984, 43, 519–529 Zbl0586.46021
  5. [5] Rzaev R.M., On some properties of Riesz potentials in terms of the higher order mean oscillation, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 1996, 4, 89–99 (in Russian) 
  6. [6] Rzaev R.M., A multidimensional singular integral operator in spaces defined by conditions on the k-th order mean oscillation, Dokl. Akad. Nauk, 1997, 356, 602–604 (in Russian) Zbl1048.42015
  7. [7] Rzaev R.M., Integral operators in spaces defined by conditions on the mean oscillation of functions and some applications, Diss. Doct. Physical and Math. Sci., Baku, 1998 (in Russian) 
  8. [8] Rzaev R.M., Local properties of singular integrals in terms of mean oscillation, Proc. Inst. Math. Mech. Acad. Sci. Azerb., 1998, 8, 179–185 (in Russian) 
  9. [9] Rzaev R.M., On some maximal functions, measuring smoothness, and metric characteristics, Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 1999, 19, 118–124 
  10. [10] Rzaev R.M., Aliyeva L.R., On some local properties of functions, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 2005, 25, 111–118 Zbl1102.41006
  11. [11] Spanne S., Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa, 1965, 19, 593–608 Zbl0199.44303
  12. [12] Stein E.M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New J., 1970 Zbl0207.13501

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