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Complex Analysis and Geometry Seminar

Sparse domination of singular integral operators

Yumeng Ou: MIT

Location:  Hill 705
Date & time: Friday, 24 March 2017 at 10:30AM - 10:31AM

It is discovered recently by Lacey (and refined by Lerner) that Calder'on-Zygmund (CZ) operators, which are a priori non-local, can be dominated pointwisely by a class of local, positive, sparse averaging operators. This in particular implies sharp weighted norm inequalities for CZ operators. In a series of joint works with A. Culiuc and F. Di Plinio, we show that sparse domination can be obtained in contexts well beyond CZ theory, such as for rough homogeneous singular integrals, Bochner-Riesz multipliers, and even modulation invariant multilinear singular integrals including the bilinear Hilbert transforms. Many new sharp weighted estimates for these operators then follow immediately.

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