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

• Autorzy: Rahim Rzaev , Lala Aliyeva
• 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.

Słowa kluczowe

EN

mean oscillation; local properties of functions; singular integrals

Kategorie tematyczne

• 26B35: Special properties of functions of several variables, H\"older conditions, etc.
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 4
• Strony: 595-609

Daty

wydano

2008-12-01

online

2008-10-08

Twórcy

autor

Rahim Rzaev

• Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan

autor

Lala Aliyeva

• 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

Identyfikatory

DOI

10.2478/s11533-008-0046-4