An inequality for multiple convolutions with respect to Dirichlet probability measure |
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Institution: | Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, United States |
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Abstract: | A sharp multiple convolution inequality with respect to Dirichlet probability measure on the standard simplex is presented. Its discrete version in terms of the negative binomial coefficients is proved as well. The new bounds for the Dirichlet distribution and iterated convolutions are obtained as the consequences of the main result. Also some binomial, exponential, and generalized hypergeometric applications are discussed. |
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Keywords: | Convolutions Weighted norm inequalities Euler's integrals Dirichlet distribution Dirichlet averages Hypergeometric functions |
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