Chen, Lüping; Zhong, Tongde; Qian, Tao Higher order boundary integral formula and integro-differential equation on Stein mainfolds. (English) Zbl 1275.32005 Complex Anal. Oper. Theory 6, No. 2, 447-464 (2012). Summary: This paper deals with boundary value properties and higher order singular integro-differential equations. On Stein manifolds, the Hadamard principal value, the Plemelj formula and the composite formula for higher order Bochner-Martinelli type integrals are given. As an application, the composite formula is used for discussing the solution of the higher order singular integro-differential equation. Cited in 2 Documents MSC: 32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) 32Q28 Stein manifolds 32E10 Stein spaces Keywords:Stein manifold; higher order singular integral; Bochner-Martinelli integral; Plemelj formula; integro-differential equation PDFBibTeX XMLCite \textit{L. Chen} et al., Complex Anal. Oper. Theory 6, No. 2, 447--464 (2012; Zbl 1275.32005) Full Text: DOI References: [1] Lu Q.K., Zhong T.D.: An extension of the Privalov theorem. Acta Math. Sin. 7, 144–165 (1957) (in Chinese) [2] Zhong T.D.: Integral Representation of Functions of Several Complex Variables and Multidimensional Singular Integral Equations. Xiamen University Press, Xiamen (1986) (in Chinese) [3] Zhong T.D.: Holomorphic Extension on Stein Manifolds. Research Report No. 10, Mittag-Leffler Institute, Stockholm (1987) · Zbl 0655.32005 [4] Qian T., Zhong T.D.: The differential integral equations on smooth closed orientable manifolds. Acta Math. Sci. 21, 1–8 (2001) · Zbl 0995.32004 [5] Chen L.P., Zhong T.D.: Regularization for high order singular integral equations. Integr Equ Oper Theory 62(1), 65–76 (2008) · Zbl 1181.32013 · doi:10.1007/s00020-008-1606-5 [6] Chen L.P., Zhong T.D.: Higher order singular integral equations on complex hypersphere. Acta Math Sci 30B(5), 1785–1792 (2010) · Zbl 1240.32005 [7] Henkin G.M., Leiterer J.: Theory of Functions on Complex Manifolds. Akademie-Verlag and Birkhäuser-Verlag, Berlin (1984) [8] Zhong T.D., Huang S.: Complex Analysis in Several Variables. Hebei Educational Press, Shijiazhuang (1990) (in Chinese) [9] Zhong T.D.: Singular integral equations on Stein manifolds. J. Xiamen Univ. Nat. Sci. 30(3), 231–234 (1991) · Zbl 0745.32003 [10] Zhong T.D.: Singular Integrals and Integral Representations in Several Complex Variables. Contemporary Mathematics, vol. 142, pp. 151–173. The American Mathematical Society, Providence (1993) · Zbl 0821.32003 [11] Kytmanov A.M.: The Bochner–Martinelli Integral and its Applications. Birkhäuser Verlag, Basel (1995) · Zbl 0834.32001 [12] Hadamard, J.: Lecture on Cauchy’s Problem in Linear Partial Differential Equations. New York (1952) · Zbl 0049.34805 [13] Appell J.M., Kalitvin A.S., Zabrejko P.P.: Partial Integral Operators and Integro-Differential Equations. Marcel Dekker, New York (2000) · Zbl 0949.45006 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.