| Project/Area Number |
23KF0188
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Multi-year Fund |
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| Section | 外国 |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Saitama University |
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Principal Investigator |
BEZ NEAL 埼玉大学, 理工学研究科, 教授 (30729843)
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| Co-Investigator(Kenkyū-buntansha) |
GAUVAN ANTHONY 埼玉大学, 理工学研究科, 外国人特別研究員
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| Project Period (FY) |
2023-11-15 – 2026-03-31
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| Project Status |
Granted (Fiscal Year 2023)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2025: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2024: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2023: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | Maximal operator / Geometric inequality |
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| Outline of Research at the Start |
This research project aims to significantly advance the current theory of geometric maximal operators by establishing optimal weak-type estimates. The framework is wide and includes maximal operators given by averages over certain families of rectangles and lower-dimensional objects such as curves.
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| Outline of Annual Research Achievements |
The main focus of this research project is the study of maximal operators which are associated with averages over certain regions in euclidean space. This includes maximal averages over certain families of rectangles and directional maximal operators associated with certain families of curves and line segments. The period of research associated with this report is roughly four months and so it can be considered to be in its relatively early stages of development. Progress towards the main goals of the research project is ongoing and it is expected that concrete research achievements in this direction can be reported on later in the project.
The project is also naturally evolving to a certain extent and, since the project began, research discussions have resulted in new directions of exploration. These are related goals in the sense that they involve the study of inequalities of an intrinsic geometric nature. Extremely pleasing progress has been made on these problems and it is expected that concrete research achievements in these directions will be achieved later in the project.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Given the highly ambitious nature of the research project and the relatively short period of research associated with this report, it is too be expected that progress is ongoing and tangible outcomes will be available further into the project.
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| Strategy for Future Research Activity |
Research will continue towards the ambitious goals of the initial research proposal on geometric maximal operators. The new lines of research on related geometric inequalities which have opened up since the project began will also be actively explored in this next phase of the project.
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