2023 Fiscal Year Research-status Report
Endpoint estimates for geometric maximal operators
| Project/Area Number |
23KF0188
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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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| Keywords | Maximal operator / Geometric inequality |
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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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| Causes of Carryover |
The postdoctoral researcher now has at least two visits to Europe and one visit to Australia planned for FY2024. One visit to Europe is for two consecutive summer schools in Bonn (8-12 July and 15-19 July). The timing of the decision by the summer school organizers regarding the postdoctoral researcher's participation at the summer schools made it difficult to plan use of the funds. It was decided that the best use of the funds would be to carry over some into FY2024 to support such long-haul trips.
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