Singular integrals in uniformly convex spaces


题目:Singular integrals in uniformly convex spaces

报告人:Tuomas HytönenAalto University

摘要:We consider the action of finitely truncated singular integral operators on functions taking values in a Banach space. Such operators are bounded for any Banach space, but we show a quantitative improvement over the trivial bound in any space renormalizable with uniformly convex norm, which is equivalent to probabilistic estimates known as martingale type and cotype. The proof, which is based on the representation of a singular integral as an average of dyadic model operators over a random choice of the dyadic decomposition of the domain, follows the broad outline of recent works on similar results for genuinely singular (non-truncated) operators in the narrower class of UMD (unconditional martingale differences) spaces, but our setting, the main theorem, and some aspects of its proof, are new. This is based on arXiv:2310.08926.




报告人简介:Tuomas Hytönen is Professor at Aalto University, Finland, since 2024. He obtained his doctorate from the Helsinki University of Technology in 2003 and was previously Professor at the University of Helsinki in 2015–2023. Hytönen is an author or co-author of over 100 research papers and a co-author of a series of three monographs on Analysis in Banach spaces.  He is perhaps best known for his solution of the A₂ conjecture on sharp weighted norm inequalities, about which he gave an invited talk at the International Congress of Mathematicians in 2014. Hytönen serves in the editorial boards of several journals, including Acta Mathematica and the Journal of European Mathematical Society.

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