On the compactness of embeddings for a class of weighted Orlicz-Sobolev sequence spaces
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917967881568256 |
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| author | Vuillermot, Pierre-A. |
| author_facet | Vuillermot, Pierre-A. |
| contents | In this article we introduce a new scale of weighted Orlicz-Sobolev sequence spaces generated by a class of suitable Orlicz functions and prove various continuity and compactness criteria for them. In a nutshell, continuity is a consequence of pointwise comparison between Orlicz functions while compactness follows from the combination of the existence of a Schauder basis in the spaces under consideration with a condition on the generating Orlicz functions regarding their local behavior in a small neighborhood of the origin. We illustrate our results by means of several concrete examples and also mention some open questions along the way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the compactness of embeddings for a class of weighted Orlicz-Sobolev sequence spaces Vuillermot, Pierre-A. Functional Analysis Primary 46B50, secondary 46E30, 46E39 In this article we introduce a new scale of weighted Orlicz-Sobolev sequence spaces generated by a class of suitable Orlicz functions and prove various continuity and compactness criteria for them. In a nutshell, continuity is a consequence of pointwise comparison between Orlicz functions while compactness follows from the combination of the existence of a Schauder basis in the spaces under consideration with a condition on the generating Orlicz functions regarding their local behavior in a small neighborhood of the origin. We illustrate our results by means of several concrete examples and also mention some open questions along the way. |
| title | On the compactness of embeddings for a class of weighted Orlicz-Sobolev sequence spaces |
| topic | Functional Analysis Primary 46B50, secondary 46E30, 46E39 |
| url | https://arxiv.org/abs/2503.19454 |