Informace o publikaci

Optimality problems in Orlicz spaces

Logo poskytovatele


Rok publikování 2023
Druh Článek v odborném periodiku
Časopis / Zdroj Advances in Mathematics
Fakulta / Pracoviště MU

Fakulta informatiky

Klíčová slova Orlicz space; Rearrangement-invariant space; Optimality; Sobolev embedding; Maximal operator; Laplace transform
Přiložené soubory
Popis 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. (c) 2023 Elsevier Inc. All rights reserved.
Související projekty:

Používáte starou verzi internetového prohlížeče. Doporučujeme aktualizovat Váš prohlížeč na nejnovější verzi.

Další info