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**Sample text**

Let g be one of the functions hI, h2,... hm' HI, H 2,... ,Hn - m and L ::; N. 1 for + h) = L 101~N 8 0 I(xo) h~ 0:. Ilhll oo < 0 IRN(X, h)1 ::; e N+1 oN L (0: 101=N+I Therefore log IRN(x, h)1 + RN(X, h) +: -1) . )8-1 . = (s - t + o(I))Nlog N and claim follows. References [1] H. J. Alexander and B. A. Taylor, Comparison of two capacities in en, Math. Z. 186 (1984), no. 3, 407-417. [2] K. I. Babenko, On the entropy of a class of analytic functions, Nauchn. Dokl. Vyssh. Shkol. Ser. -Mat. Nauk (1958), no.

Writing on each boundary component z(s) = r(s)eib(sl, substituting and separating real and imaginary parts yields r' = cos a. Since each component is a closed curve, it cannot be a spiral, cos a must be zero, thus each component is a circle centered at the origin. Moreover, the case of the annulus is ruled out because ~; changes directions between the two boundary circles, hence Izl = canst on r, and G is a disk centered at the origin. CASE 2. p> 1, p rt- N If p is not an integer S(Z)p-l may be multivalued.

Baouendi, P. Ebenfelt, and L. P. Rothschild, Real submanifolds in complex space and their mappings, Princeton Mathematical Series, vol. 47, Princeton University Press, Princeton, NJ, 1999. [4] E. , vol. 919, Springer, Berlin, 1982, pp. 294-323. PLURIPOLARITY OF MANIFOLDS 33 [5] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), no. 1-2, 1-40. [6] D. Coman, N. Levenberg, and E. A. Poletsky, Quasianalyticity and pluripolarity, J. Amer. Math. Soc. 18 (2005), no.