Hölder estimates on higher derivatives of the solution for ∂-equation with Ck-data in strongly pseudoconvex domain

Tetsuo SAITO

doi:10.2969/jmsj/03220213

Hölder estimates on higher derivatives of the solution for ∂-equation with C^k-data in strongly pseudoconvex domain

Tetsuo SAITO

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 2 Pages 213-231

DOI https://doi.org/10.2969/jmsj/03220213

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Published: 1980 Received: August 22, 1977 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Hölder estimates on higher derivatives solution for ∂-equation with C^k-data strongly pseudoconvex domain
Right : Hölder estimates on higher derivatives of the solution for ∂-equation with C^k-data in strongly pseudoconvex domain

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains, Mat. Sb., 78 (1969), 661-632; Math. USSR Sb., 7, 597-616.
2) G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and applications to ∂-problems, Mat. Sb., 82 (1970), 300-308; Math. USSR. Sb., 11, 273-281.
3) G. M. Henkin, and A. V. Romanov, Exact Hölder estimates of the ∂-equation, Izv. Akad. SSSR, Ser. Mat., 35 (1971), 1171-1183.
4) N. Kerzman, Hölder and L^p estimates for the solutions of ∂u=f in strongly pseudoconvex domains, Comm. Pure Appl. Math., 24 (1971), 301-379.
5) R. M. Range and Y. T. Siu, Uniform estimates for the ∂-equation on domains with piecewise smooth strictly pseudoconvex boundaries, Math. Ann., 206 (1974), 325-354.
6) Y. T. Siu, The ∂-problem with uniform bounds on derivatives, Math. Ann., 207 (1974), 163-176.
7) S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.

Right : [1] G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains, Mat. Sb., 78 (1969), 661-632; Math. USSR Sb., 7, 597-616.
[2] G. M. Henkin, Integral representations of functions holomorphic in strictly pseudoconvex domains and applications to ∂-problems, Mat. Sb., 82 (1970), 300-308; Math. USSR. Sb., 11, 273-281.
[3] G. M. Henkin, and A. V. Romanov, Exact Hölder estimates of the ∂-equation, Izv. Akad. SSSR, Ser. Mat., 35 (1971), 1171-1183.
[4] N. Kerzman, Hölder and L^p estimates for the solutions of ∂u=f in strongly pseudoconvex domains, Comm. Pure Appl. Math., 24 (1971), 301-379.
[5] R. M. Range and Y. T. Siu, Uniform estimates for the ∂-equation on domains with piecewise smooth strictly pseudoconvex boundaries, Math. Ann., 206 (1974), 325-354.
[6] Y. T. Siu, The ∂-problem with uniform bounds on derivatives, Math. Ann., 207 (1974), 163-176.
[7] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.

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