Sobolev space projections in strictly pseudoconvex domains

Boas, Harold P.

doi:10.1090/S0002-9947-1985-0773058-4

Sobolev space projections in strictly pseudoconvex domains
HTML articles powered by AMS MathViewer

by Harold P. Boas PDF

Trans. Amer. Math. Soc. 288 (1985), 227-240 Request permission

Abstract:

The orthogonal projection from a Sobolev space ${W^s}(\Omega )$ onto the subspace of holomorphic functions is studied. This analogue of the Bergman projection is shown to satisfy regularity estimates in higher Sobolev norms when $\Omega$ is a smooth bounded strictly pseudoconvex domain in ${{\mathbf {C}}^n}$.

References

Robert A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0450957
N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 51437, DOI 10.1090/S0002-9947-1950-0051437-7
David E. Barrett, Regularity of the Bergman projection on domains with transverse symmetries, Math. Ann. 258 (1981/82), no. 4, 441–446. MR 650948, DOI 10.1007/BF01453977
Steven R. Bell, Biholomorphic mappings and the $\bar \partial$-problem, Ann. of Math. (2) 114 (1981), no. 1, 103–113. MR 625347, DOI 10.2307/1971379
Steven R. Bell, A representation theorem in strictly pseudoconvex domains, Illinois J. Math. 26 (1982), no. 1, 19–26. MR 638551
Steven R. Bell and Harold P. Boas, Regularity of the Bergman projection and duality of holomorphic function spaces, Math. Ann. 267 (1984), no. 4, 473–478. MR 742893, DOI 10.1007/BF01455965
Steven Bell and David Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), no. 2, 385–396. MR 659947
Stefan Bergman, The kernel function and conformal mapping, Second, revised edition, Mathematical Surveys, No. V, American Mathematical Society, Providence, R.I., 1970. MR 0507701
Harold P. Boas, Holomorphic reproducing kernels in Reinhardt domains, Pacific J. Math. 112 (1984), no. 2, 273–292. MR 743985

Regularity of the Szegö projection in domains of finite type

Boundary invariants of pseudoconvex domains

John P. D’Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), no. 3, 615–637. MR 657241, DOI 10.2307/2007015
Steven Bell and David Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), no. 2, 385–396. MR 659947
Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
Norberto Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149–158. MR 294694, DOI 10.1007/BF01419622

Harmonic integrals on strongly pseudoconvex manifolds

78

79

J.-L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Band 181, Springer-Verlag, New York-Heidelberg, 1972. Translated from the French by P. Kenneth. MR 0350177
D. H. Phong and E. M. Stein, Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains, Duke Math. J. 44 (1977), no. 3, 695–704. MR 450623