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Sparse Domination Of The Martingale Transform, Michael Scott Kutzler
Sparse Domination Of The Martingale Transform, Michael Scott Kutzler
Mathematics & Statistics ETDs
Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.
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