Local Morrey and Campanato Spaces on Quasimetric Measure Spaces
We define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal oper...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/172486 |
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| _version_ | 1832568081913741312 |
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| author | Krzysztof Stempak Xiangxing Tao |
| author_facet | Krzysztof Stempak Xiangxing Tao |
| author_sort | Krzysztof Stempak |
| collection | DOAJ |
| description | We define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal operators associated to them are studied. In numerous remarks, we relate the developed theory, mostly in the “global” case, to the cases existing in the literature. We also suggest a coherent theory of generalized Morrey and Campanato spaces on open proper subsets of Rn. |
| format | Article |
| id | doaj-art-6c99b7c27a15444796c261069177a6eb |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-6c99b7c27a15444796c261069177a6eb2025-02-03T00:59:52ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/172486172486Local Morrey and Campanato Spaces on Quasimetric Measure SpacesKrzysztof Stempak0Xiangxing Tao1Instytut Matematyki i Informatyki, Politechnika Wrocławska, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, PolandDepartment of Mathematics, Zhejiang University of Science and Technology, Hangzhou, Zhejiang 310023, ChinaWe define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal operators associated to them are studied. In numerous remarks, we relate the developed theory, mostly in the “global” case, to the cases existing in the literature. We also suggest a coherent theory of generalized Morrey and Campanato spaces on open proper subsets of Rn.http://dx.doi.org/10.1155/2014/172486 |
| spellingShingle | Krzysztof Stempak Xiangxing Tao Local Morrey and Campanato Spaces on Quasimetric Measure Spaces Journal of Function Spaces |
| title | Local Morrey and Campanato Spaces on Quasimetric Measure Spaces |
| title_full | Local Morrey and Campanato Spaces on Quasimetric Measure Spaces |
| title_fullStr | Local Morrey and Campanato Spaces on Quasimetric Measure Spaces |
| title_full_unstemmed | Local Morrey and Campanato Spaces on Quasimetric Measure Spaces |
| title_short | Local Morrey and Campanato Spaces on Quasimetric Measure Spaces |
| title_sort | local morrey and campanato spaces on quasimetric measure spaces |
| url | http://dx.doi.org/10.1155/2014/172486 |
| work_keys_str_mv | AT krzysztofstempak localmorreyandcampanatospacesonquasimetricmeasurespaces AT xiangxingtao localmorreyandcampanatospacesonquasimetricmeasurespaces |