ncku-talk2017-11-23

Colloquium

DATE 2017-11-23　16:10-17:00

PLACE 數學館3174教室

SPEAKER 沈俊嚴教授（臺灣大學數學系）

TITLE Nonhomogeneous Harmonic Analysis

ABSTRACT One of the major open problems in nonhomogeneous Harmonic analysis is to find the necessary and sufficient conditions for the boundedness of two weights inequality for singular integrals. In this talk, we will first discuss the famous two weights problem for the Hilbert transform and outline our proof that settles this longstanding open problem. We then discuss some of the main difficulties for higher dimensional singular integrals. Some of the important applications to other fields will be also discussed, in particular an application of our T1 theorem for the Cauchy transform in the complex plane settles the open problem: the embedding problem for the model spaces.

Colloquium

DATE	2017-11-23　16:10-17:00

PLACE	數學館3174教室

SPEAKER	沈俊嚴教授（臺灣大學數學系）

TITLE	Nonhomogeneous Harmonic Analysis

ABSTRACT	One of the major open problems in nonhomogeneous Harmonic analysis is to find the necessary and sufficient conditions for the boundedness of two weights inequality for singular integrals. In this talk, we will first discuss the famous two weights problem for the Hilbert transform and outline our proof that settles this longstanding open problem. We then discuss some of the main difficulties for higher dimensional singular integrals. Some of the important applications to other fields will be also discussed, in particular an application of our T1 theorem for the Cauchy transform in the complex plane settles the open problem: the embedding problem for the model spaces.