It was recently proved by Bayart et al. that the complex polynomial Bohnenblust-Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if D R,m stands for the real Bohnenblust-Hille constant for m-homogeneous polynomials, then lim sup m D 1/m R,m = 2.2010 Mathematics Subject Classification. 46G25, 47L22, 47H60.
The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the real setting if we relax the analyticity hypothesis on the function to infinitely many times differentiability. In fact, we construct an algebra of functions A enjoying the following properties: (i)
Abstract. In this paper we prove that the complex polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in C 2 is exactly 4 3 2 . We also give the exact value of the real polynomial Bohnenblust-Hille constant for 2-homogeneous polynomials in R 2 . Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in R 2 of higher degrees.
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