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Proceedings of the American Mathematical Society

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The Poincaré inequality and entire functions

Author: J. Michael Pearson
Journal: Proc. Amer. Math. Soc. 118 (1993), 1193-1197
MSC: Primary 32A15
MathSciNet review: 1152286
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Abstract: Inequalities for spaces of entire functions on $ {{\mathbf{C}}^n}$, which generalize the Poincaré inequality for Gaussian measure, are obtained. The relationship between these inequalities and hypercontractive estimates for diffusion semigroups are discussed.

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