This Project Grant award, funded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports fundamental research on sparseness and Bellman functions in harmonic analysis. The $216,509 award to the University of Wyoming aims to advance the understanding of the Hilbert transform and other important operators in harmonic analysis through the development of new techniques that bridge the Bellman function method and the sparse operator domination approach. Key research activities include:
- Settling open problems related to weighted inequalities and the dyadic square function, a foundational operator in Littlewood-Paley theory
- Building connections between the Bellman function method and sparse operator techniques to create a new analytical framework
- Organizing activities and training graduate students in the field of harmonic analysis
This award reflects NSF's mission to strengthen the nation's scientific enterprise and enable advancements in mathematical and physical sciences that can have broader societal impacts. The project is scheduled to run from February 2025 to July 2026.
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