## 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**
—, - 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
J. I. Kohn, - 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**

*Regularity of the Szegö projection in domains of finite type*, in preparation. D. Catlin,

*Boundary invariants of pseudoconvex domains*, Ann. of Math. (in press).

*Harmonic integrals on strongly pseudoconvex manifolds*, I, II, Ann. of Math.

**78**(1963), 112-148;

**79**(1964), 450-472.

## Additional Information

- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**288**(1985), 227-240 - MSC: Primary 32H05; Secondary 32F15
- DOI: https://doi.org/10.1090/S0002-9947-1985-0773058-4
- MathSciNet review: 773058