Sobolev spaces and potential spaces associated to Hermite polynomials expansions

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Sobolev spaces and potential spaces associated to Hermite polynomials expansions

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Title: Sobolev spaces and potential spaces associated to Hermite polynomials expansions
Author: López P., Iris A.
Abstract: El objetivo de este trabajo es estudiar la relación existente entre los espacios potenciales y los espacios de Sobolev, inducidos por el operador diferencial Ornstein-Uhlenbeck y asociados a las expansiones polinomiales de Hermite, donde consideramos la medida gaussiana multidimensional. Por medio de métodos analíticos probamos que los espacios potenciales y los espacios de Sobolev son espacios con normas equivalentes.The aim of this paper is to study the relation existing between potential spaces and Sobolev spaces, induced by the Ornstein-Uhlenbeck differential operator and associated to Hermite polynomials expansions, where we consider the multidimensional Gaussian measure. By means of analytical methods we prove that potential spaces and Sobolev spaces are spaces with equivalent norms.
URI: http://hdl.handle.net/10662/8629
Date: 2018


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