The Sparse T1 Theorem

Abstract

We impose standard $T1$-type assumptions on a Calderón-Zygmund operator $T$, and deduce that for bounded compactly supported functions $f,g$ there is a sparse bilinear form $\Lambda$ so that $$|⟨Tf,g⟩|\lesssim \Lambda (f,g).$$ The proof is short and elementary. The sparse bound quickly implies all the standard mapping properties of a Calderón-Zygmund on a (weighted) $L^p$ space.

To appear in Houston Math J

References in corpus (4)

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• Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination
• Uniform sparse domination of singular integrals via dyadic shifts
• A sparse estimate for multisublinear forms involving vector-valued maximal functions
• Endpoint sparse bounds for Walsh-Fourier multipliers of Marcinkiewicz type
• A sparse quadratic $T1$ theorem
• Bilinear representation theorem
• Sparse domination of Hilbert transforms along curves
• Sparse bounds for discrete singular Radon transforms
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