On the Optimal Domain of the Laplace Transform

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• 作者：O. Galdames Bravo
• 关键词：Banach function space ; Laplace transform ; Optimal domain ; P ; th power factorization
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：389-408
• 全文大小：
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：40

文摘

We consider optimal domain as the largest order continuous Banach function space where the Laplace transform can be extended, when it is defined from the space of bounded functions into a suitable weighted \(L^p\)-space. We prove that \(L^p(0,\infty )\) is continuously embedded into such optimal domain. Finally, we apply the technique of extension the so-called p-th power factorization to this scheme and obtain new domains for the Laplace transform. We also provide a concrete example of computation of the optimal domain.