Yuping Zhai

Professor Leslie Cheng

Math Department

Boundedness of Oscillatory Singular Integrals

 

Over the summer, I will be conducting research with Professor Leslie Cheng in the field of functional spaces and applications. Since I have some background in graduate analysis but little understanding in harmonic analysis, I will begin my summer research on reading a paper on the above topic: Weighted Estimates for Oscillatory Singular Integrals.  

 

The research I will conduct will focus on the study of oscillatory singular integral operators and Marcinkiewicz integral operators. I will especially focus on the boundedness of oscillatory singular integral operators and Marcinkiewicz integral operators. Based on previous results by many mathematicians on the above operators, I would like to extend results on different situations. I will do all of this research in understanding the proofs of related theorems and making proofs on extended results.