A Sobolev inequality for pluriharmonic functions
by Steven R. Bell PDF
Proc. Amer. Math. Soc. 85 (1982), 350-352 Request permission
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.
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
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Journal: Proc. Amer. Math. Soc. 85 (1982), 350-352
MSC: Primary 32A40; Secondary 31C10
MathSciNet review: 656100