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arXiv · 2201.06530

Paraproducts, Bloom BMO and Sparse BMO Functions

Valentia Fragkiadaki·Irina Holmes Fay
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Abstract

We address $L^p(\mu)\rightarrow L^p(\lambda)$ bounds for paraproducts in the Bloom setting. We introduce certain "sparse BMO" functions associated with sparse collections with no infinitely increasing chains, and use these to express sparse operators as sums of paraproducts and martingale transforms -- essentially, as Haar multipliers -- as well as to obtain an equivalence of norms between sparse operators $\mathcal{A}_\mathcal{S}$ and compositions of paraproducts $\Pi^*_a\Pi_b$.

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Valentia Fragkiadaki, Irina Holmes Fay. 2022-01-17. Paraproducts, Bloom BMO and Sparse BMO Functions. https://arxiv.org/abs/2201.06530

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