An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces \(L^{1,\nu,\beta}(G)\) (Q1012458)
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scientific article; zbMATH DE number 5545483
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces \(L^{1,\nu,\beta}(G)\) |
scientific article; zbMATH DE number 5545483 |
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An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces \(L^{1,\nu,\beta}(G)\) (English)
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21 April 2009
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The paper provides an elementary proof of Sobolev embeddings for \(\alpha-\)Riesz potentials \((0\leq \alpha<n)\) into the Morrey space \(L^{1,\nu,\beta}(G)\), where \(G\subset \mathbb{R}^n\) is a bounded open set, \(\alpha\leq \nu<n\). The results extend those from [\textit{J. Serrin}, A remark on the Morrey potential. Control methods in PDE-dynamical systems. AMS-IMS-SIAM joint summer research conference, Snowbird, UT, USA, July 3--7, 2005. Providence, RI: American Mathematical Society (AMS). Contemporary Mathematics 426, 307--315 (2007; Zbl 1129.31003)].
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Riesz potentials
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Sobolev inequality
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Morrey space
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