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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
DOI: https://doi.org/10.1090/S0002-9939-1993-1152286-2
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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DOI: https://doi.org/10.1090/S0002-9939-1993-1152286-2
Article copyright: © Copyright 1993 American Mathematical Society

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