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arXiv · 2406.16912

On Tempered Ultradistributions in Classical Sobolev Spaces

A. U. Amaonyeiro·M. E. Egwe
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Abstract

We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$ for $1\leq p\leq \infty$ is characterized. Moreover, we also consider some Sobolev embedding theorems involving rapidly decreasing functions, and finally, we prove the extension of Rellich's compactness theorem.

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A. U. Amaonyeiro, M. E. Egwe. 2024-06-06. On Tempered Ultradistributions in Classical Sobolev Spaces. https://arxiv.org/abs/2406.16912

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