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Michael T. Lacey and Scott Spencer
Sparse bounds for oscillatory and random singular integrals view print
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| Published: |
January 25, 2017 |
| Keywords: |
Sparse bound, weighted inequalities, oscillatory singular integrals, discrete singular integrals, random |
| Subject: |
Primary: 42B20. Secondary: 42B25 |
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Abstract
Let TPf(x) = ∫eiP(y)K(y)f(x-y) dy , where
K(y) is a smooth Calderón-Zygmund kernel on Rn, and P be a polynomial.
We show that there is a sparse bound for the bilinear form < TP f, g >.
This in turn easily implies Ap 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.
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| Acknowledgements
Research supported in part by grant NSF-DMS 1265570 and NSF-DMS-1600693
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| 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
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