Matuszewska–Orlicz indices of the Sobolev conjugate Young function
In this note we study the Matuszewska–Orlicz indices of Young and φ-functions and their conjugates. It is known, for example, that the index at zero of the inverse of a φ-function corresponds to the reciprocal of the index at infinity of the φ-function itself, and vice-versa. Likewise, the index at...
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2021-06-01
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doaj-bc083a4145b940a99c7b0d373dffae192021-06-05T06:10:59ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812021-06-013100029Matuszewska–Orlicz indices of the Sobolev conjugate Young functionWaldo Arriagada0Department of Applied Mathematics, Khalifa University, Al Zafranah, P.O. Box 127788, Abu Dhabi, United Arab EmiratesIn this note we study the Matuszewska–Orlicz indices of Young and φ-functions and their conjugates. It is known, for example, that the index at zero of the inverse of a φ-function corresponds to the reciprocal of the index at infinity of the φ-function itself, and vice-versa. Likewise, the index at zero of the complementary Young function matches the Hölder conjugate of the index at infinity and the same holds for the opposite index. In this article we prove that the Matuszewska–Orlicz indices of the Sobolev conjugate Young function are equal to the Sobolev conjugate of the corresponding indices of the Young function. We then provide some examples as well which highlight the importance of an asymptotic condition in connection with Karamata theorem. Finally, we present a few examples and applications in the context of Orlicz spaces.http://www.sciencedirect.com/science/article/pii/S2666818121000097φ-functionAsymptotic homogeneityOrlicz–Sobolev space |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Waldo Arriagada |
spellingShingle |
Waldo Arriagada Matuszewska–Orlicz indices of the Sobolev conjugate Young function Partial Differential Equations in Applied Mathematics φ-function Asymptotic homogeneity Orlicz–Sobolev space |
author_facet |
Waldo Arriagada |
author_sort |
Waldo Arriagada |
title |
Matuszewska–Orlicz indices of the Sobolev conjugate Young function |
title_short |
Matuszewska–Orlicz indices of the Sobolev conjugate Young function |
title_full |
Matuszewska–Orlicz indices of the Sobolev conjugate Young function |
title_fullStr |
Matuszewska–Orlicz indices of the Sobolev conjugate Young function |
title_full_unstemmed |
Matuszewska–Orlicz indices of the Sobolev conjugate Young function |
title_sort |
matuszewska–orlicz indices of the sobolev conjugate young function |
publisher |
Elsevier |
series |
Partial Differential Equations in Applied Mathematics |
issn |
2666-8181 |
publishDate |
2021-06-01 |
description |
In this note we study the Matuszewska–Orlicz indices of Young and φ-functions and their conjugates. It is known, for example, that the index at zero of the inverse of a φ-function corresponds to the reciprocal of the index at infinity of the φ-function itself, and vice-versa. Likewise, the index at zero of the complementary Young function matches the Hölder conjugate of the index at infinity and the same holds for the opposite index. In this article we prove that the Matuszewska–Orlicz indices of the Sobolev conjugate Young function are equal to the Sobolev conjugate of the corresponding indices of the Young function. We then provide some examples as well which highlight the importance of an asymptotic condition in connection with Karamata theorem. Finally, we present a few examples and applications in the context of Orlicz spaces. |
topic |
φ-function Asymptotic homogeneity Orlicz–Sobolev space |
url |
http://www.sciencedirect.com/science/article/pii/S2666818121000097 |
work_keys_str_mv |
AT waldoarriagada matuszewskaorliczindicesofthesobolevconjugateyoungfunction |
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1721396516353998848 |