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Optimality problems in Orlicz spaces
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Musil, Vít, Pick, Luboš and Takáč, Jakub (2023) Optimality problems in Orlicz spaces. Advances in Mathematics, 432 . 109273. doi:10.1016/j.aim.2023.109273 ISSN 0001-8708.
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Official URL: https://doi.org/10.1016/j.aim.2023.109273
Abstract
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the mutual relationship between the data and solution quality. The optimality of the obtained results deserves a special focus. It requires a careful choice of families of function spaces balancing between their expressivity, i.e. the ability to capture fine properties of the model, and their accessibility, i.e. its technical difficulty for practical use. This paper presents a unified and general approach to optimality problems in Orlicz spaces. Orlicz spaces are parametrized by a single convex function and neatly balance the expressivity and accessibility. We prove a general principle that yields an easily verifiable necessary and sufficient condition for the existence or the non-existence of an optimal Orlicz space in various tasks. We demonstrate its use in specific problems, including the continuity of Sobolev embeddings and boundedness of integral operators such as the Hardy–Littlewood maximal operator and the Laplace transform.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
SWORD Depositor: | Library Publications Router | ||||||||
Journal or Publication Title: | Advances in Mathematics | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0001-8708 | ||||||||
Official Date: | 1 November 2023 | ||||||||
Dates: |
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Volume: | 432 | ||||||||
Article Number: | 109273 | ||||||||
DOI: | 10.1016/j.aim.2023.109273 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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