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Lp (1 ≤ p ≤ ∞) estimates for on a certain pseudoconvex domain in ℂn

Published online by Cambridge University Press:  22 January 2016

Kenzō Adachi  and
Hong Rae Cho
Kenzō Adachi
Affiliation:
Department of Mathematics, Nagasaki University, Nagasaki 852, Japan, k-adachi@net.nagaski-u.ac.jp
Hong Rae Cho
Affiliation:
Department of Mathematics Education, Andong National University, Andong, Kyungbuk 760-749, Korea, chohr@anu.andong.ac.kr
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Abstract

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Let Ψ ∈ C2[0,1] be a positive real valued function on (0, 1]. Under certain assumptions on Ψ, the set is a pseudoconvex domain with C2-boundary which may be infinite type. If Ψ has flatness at 0 so that then we can obtain Lp(1 ≤ p ≤ ∞) estimates for on D.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 148 , December 1997 , pp. 127 - 136
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

[1] Bruna, J. and Castillo, J., Hölder and Lp estimates for the equation in some convex domains with real analytic boundary, Math. Ann., 269 (1984), 527–539.Google Scholar
[2] Chang, D.-C., Nagel, A. and Stein, E. M., Estimates for the -Neumann problem for pseudoconvex domains in ℂ2 of finite type, Proc. Nat. Acad. Sci. USA, 85 (1988), 8771–8774.CrossRefGoogle ScholarPubMed
[3] Fornaess, J. E. and Sibony, N., Smooth pseudoconvex domains in ℂ2 for which the Corona theorem and Lp estimates for fail, Complex analysis and geometry, New York, 29 (1993), 209–222.Google Scholar
[4] Henkin, G. and Cirka, E., Boundary properties of holomorphic functions of several complex variables, J. Sovit Math., 5 (1976), 612–687.CrossRefGoogle Scholar
[5] Kerzman, N., Hölder and Lp estimates for solutions of in strongly pseudoconvex domains, Comm. Pure Appl. Math., 24 (1971), 301–379.Google Scholar
[6] Øvrelid, N., Integral representation formulas and Lp-estimates for the -equation, Math. Scand., 29 (1971), 137–160.CrossRefGoogle Scholar
[7] Polking, J. C., The Cauchy-Riemann equations in convex domains, Proc. Symp. Pure Math., 52(3) (1991), 309–322.CrossRefGoogle Scholar
[8] Range, R. M., Holomorphic functions and integral representations in several complex variables, Springer-Verlag, Berlin Heidelberg, New York, 1986.Google Scholar
[9] Verdera, J., L∞-continuity of Henkin operators solving d in certain weakly pseudoconvex domains of ℂ2 , Proc. Royal Soc. Edinburgh, 99A (1984), 25–33.CrossRefGoogle Scholar