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Sparse forms for Bochner-Riesz operators

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ASC - Approximation, sampling and compression in data science

Sparse operators are positive dyadic operators that have very nice boundedness properties. The Lp bounds and weighted Lp bounds with sharp constant are easy to obtain for these operators. In the recent years, it has been proven that singular integrals (cancellative operators) can be pointwise controlled by sparse operators. This has made the sharp weighted theory of singular integrals quite straightforward. The current efforts focus in understanding the use of sparse operators to bound rougher operators, such a oscillatory integrals. Following this direction, our goal in this talk is to describe the control of Bochner-Riesz operators by sparse operators.




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