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

Open Mathematics (2008)

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

## Access Full Article

top## Abstract

top## How to cite

topRahim 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

top- [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] Calderon A.P., Zygmund A., Local properties of solutions of elliptic partial differential equations, Studia Math., 1961, 20, 171–225 Zbl0099.30103
- [3] DeVore R., Sharpley R., Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 1984, 47, 1–115 Zbl0529.42005
- [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] 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] 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] 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] 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] 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] 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] Spanne S., Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa, 1965, 19, 593–608 Zbl0199.44303
- [12] Stein E.M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New J., 1970 Zbl0207.13501

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.