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Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

Jump theorems for the Bochner-Martinelli integral in domains with a piecewise smooth boundary are obtained. Moreover, theorem for the Bochner-Martinelli integral in domains with a piecewise smooth boundary is proved for continuous functions and also for functions from the class 𝓛p.

First Page

1

Last Page

19

References

1. Volkov E.A. Boundaries of subdomains, Hölder weight classes and solutions in these classes of the Poisson equation. Proceedings of the Steklov Institute of Mathematics, Vol. 117, 89–117 (1972).

2. Vladimirov V.S. Equations of Mathematical Physics. Moscow: Nauka, (1981).

3. Gorenskiy N.Yu. Some applications of differential properties of the distance function to open sets in ℂn. In: Some Propperties of Holomorphic Functions of many Variables. Krasnoyarsk, IFSOAN, 203–208 (1973).

4. Dautov Sh.A., Kytmanov A.M. On the boundary values of an integral of Martinelli-Bochner type. In: Some Propperties of Holomorphic Functions of many Variables. Krasnoyarsk, IFSOAN, 49–54 (1973).

5. Dzhumabaev D.Kh. Holomorphic continuation of functions from closed hypersurfaces with singular edges. Russian Mathematics, Vol. 56, Issue 1, 9–18 (2012).

6. Kakichev V.A. Character of continuity of boundary values of the Bochner-Martinelli integral. Scientific Notes of the Moscow Regional Pedagogical Institute, Vol. 96, No. 6, 145–150 (1960).

7. Kytmanov A.M. The Bochner-Martinelli Integral and its Applications. Birkhäuser Verlag, Basel, Boston, Berlin (1995).

8. Kytmanov A.M. Holomorphic extension of integrable CR-functions from part of the boundary of the domain. Mathematical notes of the Academy of Sciences of the USSR, Vol. 48, Issue 2, 761–765 (1990).

8. Kytmanov A.M. Holomorphic extension of CR-functions with singularities on a hypersurface. Mathematics of the USSR-Izvestiya, Vol. 37, No. 3, 681–691 (1990).

10. Kytmanov A.M., Aizenberg L.A. The holomorphy of continuous functions that are representable by the Martinelli-Bochner integral. Izv. Akad. Nauk Armjan. SSR Ser. Mat., Vol. 13, 158–169 (1978).

11. Kytmanov A.M., Myslivets S.G. Integral Representations and its Applications in Multidimensional Analysis. Krasnoyarsk, Siberian Federal University, (2010).

12. Prenov B.B., Tarkhanov N.N. A remark on the jump of the Bochner-Martinelli integral. Sib. Math. Journal, Vol. 30, No. 1, 199–201 (1989).

13. Sretensky L.N. Theory of Newtonian Potential. Moscow, Leningrad: Gostekhizdat, (1946).

14. Stein E., Weiss G. Introduction to Fourier analysis on Euclidean spaces. Princeton University Press, (1971).

15. Hayman W.K., Kennedy P.B. Subharmonic Functions. Academic Press London, (1976).

16. Shaimkulov B.A. On characterization of traces of holomorphic functions on some sets of uniqueness and multidimensional Carleman interpolation formulas. The dissertation for the degree of candidate of physical and mathematical sciences. Krasnoyarsk, (1988).

17. Yarmukhamedov Sh. The Bochner-Martinelli integral formula and the Phragmén-Lindelöf principle. Dokl. AN SSSR, Vol. 243, No. 6, 1414–1417 (1978).

18. Bochner S. Analitic and meromorphic continuation by means of Green's formula. Ann. Math., Vol. 44, 652–673 (1943).

19. Harvey F.R., Lowson H.B. On boundaries of complex analitic varietes. Ann. Math., Vol. 102, 223–290 (1975).

20. Look C.H., Zhong T.D. An extension of Privalov theorem. Acta Math. Sinica, Vol. 7, No. 1, 144–165 (1957).

21. Martinelli E. Alcuni teoremi integrali per le funzioni analitiche di piu variabili complesse. Mem. R. Acad. Ital., Vol. 9, 269–283 (1938).

22. Martinelli E. Sopra una dimostrazione di R. Fueter per un teorema di Hartogs. Commentarii Mathematici Helvetici, Vol. 15, No. 1, 340–349 (1942).

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