Title：Multilinear Weighted Estimates in Product Spaces

Abstract：In the one-parameter situation, the very influential paper by Lerner et. al. introduced the Muckenhoupt weights in the multilinear setting and it was shown that one can get related weighted estimates for the maximal function and singular integrals. Around 10 years ago, such class of weights were also introduced in the multilinear multi-parameter context, however, the related weighted estimates were only known for the maximal function. In this talk, I will talk about the recent progress on the multilinear weighted estimates for singular integrals in product spaces. Our result completes the qualitative weighted theory in this setting. Extrapolation gives powerful applications – for example, a free access to mixed-norm estimates in the full range of exponents.

Speaker：Li Kangwei is currently a research professor at Center for Applied Mathematics, Tianjin University.

Selected Publications：

 Li, Kangwei; Martikainen, Henri; Vuorinen, Emil Bilinear Calderón-Zygmund theory on product spaces. J. Math. Pures Appl. (9) 138 (2020), 356–412.

K. Li, H. Martikainen, E. Vuorinen, Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators, to appear in Int. Math. Res. Not., https://doi.org/10.1093/imrn/rnz072.

K. Li, S. Ombrosi, C. Pérez, Proof of an extension of E. Sawyer’s conjecture about weighted mixed weak-type estimates, Math. Ann., 374(2019), 907-929.

K. Li, H. Martikainen, Y. Ou, E. Vuorinen, Bilinear representation theorem, Trans. Amer. Math. Soc., 371(2019), 4193-4214.

K. Li, W. Sun, Weak and strong type weighted estimates for multilinear Calderón-Zygmund operators, Adv. Math., 254(2014), 736-771.

Date：3:00pm 2021-4-26（Monday）.

Venue: 56#208

Organizer：School of Mathematical Science, Yangzhou University

Students and teachers who are interested in weighted theory are welcome.