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2008 | 6 | 4 | 595-609
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
4
Strony
595-609
Opis fizyczny
Daty
wydano
2008-12-01
online
2008-10-08
Twórcy
autor
  • Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, rrzaev@rambler.ru
autor
  • Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan
Bibliografia
  • [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
  • [3] DeVore R., Sharpley R., Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 1984, 47, 1–115
  • [4] Nakai E., On the restriction of functions of bounded mean oscillation to the lower dimensional space, Arch. Math. (Basel), 1984, 43, 519–529
  • [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)
  • [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
  • [11] Spanne S., Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa, 1965, 19, 593–608
  • [12] Stein E.M., Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, New J., 1970
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0046-4
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