A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866908297440788480 |
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| author | Harjulehto, Petteri Hästö, Peter Słabuszewski, Artur |
| author_facet | Harjulehto, Petteri Hästö, Peter Słabuszewski, Artur |
| contents | Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak $Φ$-functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. Hästö, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_13331 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains Harjulehto, Petteri Hästö, Peter Słabuszewski, Artur Functional Analysis 46E30 (46E35) Conditions for harmonic analysis in generalized Orlicz spaces have been studied over the past decade. One approach involves the generalized inverse of so-called weak $Φ$-functions. It featured prominently in the monograph Orlicz Spaces and Generalized Orlicz Spaces [P. Harjulehto and P. Hästö, Lecture Notes in Mathematics, vol. 2236, Springer, Cham, 2019]. While generally successful, the inverse function formulation of the decay condition (A2) in the monograph contains a flaw, which we explain and correct in this note. We also present some new results related to the conditions, including a more general result for the density of smooth functions. |
| title | A revised condition for harmonic analysis in generalized Orlicz spaces on unbounded domains |
| topic | Functional Analysis 46E30 (46E35) |
| url | https://arxiv.org/abs/2309.13331 |