Generalized Lebesgue Points for Hajłasz Functions
Let X be a quasi-Banach function space over a doubling metric measure space P. Denote by αX the generalized upper Boyd index of X. We show that if αX<∞ and X has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Hajłasz function u∈M˙s,X. M...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/5637042 |
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| author | Toni Heikkinen |
| author_facet | Toni Heikkinen |
| author_sort | Toni Heikkinen |
| collection | DOAJ |
| description | Let X be a quasi-Banach function space over a doubling metric measure space P. Denote by αX the generalized upper Boyd index of X. We show that if αX<∞ and X has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Hajłasz function u∈M˙s,X. Moreover, if αX<(Q+s)/Q, then quasievery point is a Lebesgue point of u. As an application we obtain Lebesgue type theorems for Lorentz–Hajłasz, Orlicz–Hajłasz, and variable exponent Hajłasz functions. |
| format | Article |
| id | doaj-art-4f421a16aad447a7af9b18375a53ed8c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-4f421a16aad447a7af9b18375a53ed8c2025-02-03T06:11:01ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/56370425637042Generalized Lebesgue Points for Hajłasz FunctionsToni Heikkinen0Department of Mathematics, Aalto University, P.O. Box 11100, 00076 Aalto, FinlandLet X be a quasi-Banach function space over a doubling metric measure space P. Denote by αX the generalized upper Boyd index of X. We show that if αX<∞ and X has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Hajłasz function u∈M˙s,X. Moreover, if αX<(Q+s)/Q, then quasievery point is a Lebesgue point of u. As an application we obtain Lebesgue type theorems for Lorentz–Hajłasz, Orlicz–Hajłasz, and variable exponent Hajłasz functions.http://dx.doi.org/10.1155/2018/5637042 |
| spellingShingle | Toni Heikkinen Generalized Lebesgue Points for Hajłasz Functions Journal of Function Spaces |
| title | Generalized Lebesgue Points for Hajłasz Functions |
| title_full | Generalized Lebesgue Points for Hajłasz Functions |
| title_fullStr | Generalized Lebesgue Points for Hajłasz Functions |
| title_full_unstemmed | Generalized Lebesgue Points for Hajłasz Functions |
| title_short | Generalized Lebesgue Points for Hajłasz Functions |
| title_sort | generalized lebesgue points for hajlasz functions |
| url | http://dx.doi.org/10.1155/2018/5637042 |
| work_keys_str_mv | AT toniheikkinen generalizedlebesguepointsforhajłaszfunctions |