Article
| Title: | Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces (English) |
| Author: | Futamura, Toshihide |
| Author: | Shimomura, Tetsu |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 905-913 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove the boundedness of the generalized fractional maximal operator $M_{\alpha }$ and the generalized fractional integral operator $I_{\alpha }$ on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces. (English) |
| Keyword: | fractional integral operator |
| Keyword: | quasi-metric measure space |
| Keyword: | Hausdorff content |
| Keyword: | weak Choquet space |
| Keyword: | Ahlfors regular |
| MSC: | 28A12 |
| MSC: | 42B25 |
| MSC: | 46E30 |
| idZBL: | Zbl 07953685 |
| idMR: | MR4804967 |
| DOI: | 10.21136/CMJ.2024.0133-24 |
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| Date available: | 2024-10-03T12:40:19Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152588 |
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| Reference: | [9] Mizuta, Y., Shimomura, T., Sobukawa, T.: Sobolev's inequality for Riesz potentials of functions in non-doubling Morrey spaces.Osaka J. Math. 46 (2009), 255-271. Zbl 1186.31003, MR 2531149 |
| Reference: | [10] Orobitg, J., Verdera, J.: Choquet integrals, Hausdorff content and the Hardy-Littlewood maximal operator.Bull. Lond. Math. Soc. 30 (1998), 145-150. Zbl 0921.42016, MR 1489325, 10.1112/S0024609397003688 |
| Reference: | [11] Sawano, Y., Shimomura, T.: Fractional maximal operator on Musielak-Orlicz spaces over unbounded quasi-metric measure spaces.Result. Math. 76 (2021), Article ID 188, 22 pages. Zbl 1479.42055, MR 4305494, 10.1007/s00025-021-01490-7 |
| Reference: | [12] Watanabe, H.: Estimates of fractional maximal functions in a quasi-metric space.Nat. Sci. Rep. Ochanomizu Univ. 56 (2006), 21-31. Zbl 1113.42018, MR 2214968 |
| Reference: | [13] Watanabe, H.: Estimates of maximal functions by Hausdorff contents in a metric space.Potential Theory in Matsue Advanced Studies in Pure Mathematics 44. Mathematical Society of Japan, Tokyo (2006), 377-389. Zbl 1125.42008, MR 2279770, 10.2969/aspm/04410377 |
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