Abstract:
The integral representation obtained for smooth functions defined in strictly pseudoconvex domains in n-dimensional complex space can be considered as the “natural” extension of the well-known Cauchy–Green formula. Using this representation we succeed in obtaining a formula and uniform bound for solutions of the ¯∂-problem in strictly pseudoconvex domains.
Bibliography: 11 titles.
Citation:
G. M. Henkin, “Integral representation of functions in strictly pseudoconvex domains and applications to the ¯∂-problem”, Math. USSR-Sb., 11:2 (1970), 273–281
\Bibitem{Hen70}
\by G.~M.~Henkin
\paper Integral representation of functions in strictly pseudoconvex domains and applications to the $\overline\partial$-problem
\jour Math. USSR-Sb.
\yr 1970
\vol 11
\issue 2
\pages 273--281
\mathnet{http://mi.mathnet.ru/eng/sm3451}
\crossref{https://doi.org/10.1070/SM1970v011n02ABEH002069}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=265625}
\zmath{https://zbmath.org/?q=an:0206.09101|0216.10402}
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https://doi.org/10.1070/SM1970v011n02ABEH002069
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This publication is cited in the following 60 articles:
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Ly Kim Ha, “Ck-regularity for ∂¯-equations for a class of convex domains of infinite type in C2”, Kyoto J. Math., 60:2 (2020)
Ly Kim Ha, “Hölder and $L^p$ Estimates for the ${\bar{\partial }}$-equation in a class of convex domains of infinite type in ${\mathbb {C}}^n$”, Monatsh Math, 190:3 (2019), 517
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Equation on a Class of Convex Domains of Infinite Type in ℂ 3 $\mathbb {C}^{3}$”, Acta Math Vietnam, 44:2 (2019), 519
Henri Skoda, “A Tribute to the Memory of Gennadi Henkin”, J Geom Anal, 28:1 (2018), 688
B. Berndtsson, S. V. Kislyakov, R. G. Novikov, V. M. Polterovich, P. L. Polyakov, A. E. Tumanov, A. A. Shananin, C. L. Epstein, “Gennadi Markovich Henkin (obituary)”, Russian Math. Surveys, 72:3 (2017), 547–570
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Steven G. Krantz, Springer Monographs in Mathematics, Harmonic and Complex Analysis in Several Variables, 2017, 131
Steven G. Krantz, Springer Monographs in Mathematics, Harmonic and Complex Analysis in Several Variables, 2017, 309
Eric Amar, “On estimates for the ∂¯ equation in Stein manifolds”, Bull. London Math. Soc., 49:3 (2017), 519
Ly Kim Ha, “Tangential Cauchy–Riemann Equations on Pseudoconvex Boundaries of Finite and Infinite Type in $\mathbb {C}^2$ C 2”, Results Math, 72:1-2 (2017), 105
Steven G. Krantz, Springer Monographs in Mathematics, Harmonic and Complex Analysis in Several Variables, 2017, 115
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Loredana Lanzani, Elias M. Stein, Association for Women in Mathematics Series, 4, Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1), 2016, 179
L.K.im Ha, T.V.u Khanh, Andrew Raich, “Lpestimates for the $\bar\partial$-equation on a class of infinite type domains”, Int. J. Math, 2014, 1450106
Lanzani L., Stein E.M., “The Cauchy Integral in C-N For Domains With Minimal Smoothness”, Adv. Math., 264 (2014), 776–830
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