 

Michael T. Lacey and Scott Spencer
Sparse bounds for oscillatory and random singular integrals view print


Published: 
January 25, 2017 
Keywords: 
Sparse bound, weighted inequalities, oscillatory singular integrals, discrete singular integrals, random 
Subject: 
Primary: 42B20. Secondary: 42B25 


Abstract
Let T_{P}f(x) = ∫e^{iP(y)}K(y)f(xy) dy , where
K(y) is a smooth CalderónZygmund kernel on R^{n}, and P be a polynomial.
We show that there is a sparse bound for the bilinear form < T_{P} f, g >.
This in turn easily implies A_{p} inequalities.
The method of proof is applied in a random discrete setting, yielding the first weighted inequalities for operators defined on sparse sets of integers.


Acknowledgements
Research supported in part by grant NSFDMS 1265570 and NSFDMS1600693


Author information
Michael T. Lacey:
School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA
lacey@math.gatech.edu
Scott Spencer:
School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USA
spencer@math.gatech.edu

