A Sobolev inequality for pluriharmonic functions
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- by Steven R. Bell PDF
- Proc. Amer. Math. Soc. 85 (1982), 350-352 Request permission
Abstract:
A Sobolev inequality is proved which implies that, on a smooth bounded domain $D$ contained in ${{\mathbf {C}}^n}$, the ${L^2}$ inner product of two pluriharmonic functions is defined whenever one of them is in ${C^\infty }(D)$ and the other is dominated by some negative power of the distance to the boundary.References
- 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, Proper holomorphic mappings and the Bergman projection, Duke Math. J. 48 (1981), no. 1, 167–175. MR 610182
- Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, vol. 3, American Mathematical Society, Providence, R.I., 1979. With supplements by Lars Gȧrding and A. N. Milgram; With a preface by A. S. Householder; Reprint of the 1964 original. MR 598466
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 350-352
- MSC: Primary 32A40; Secondary 31C10
- DOI: https://doi.org/10.1090/S0002-9939-1982-0656100-3
- MathSciNet review: 656100