Sparse domination of sharp variational truncations

Abstract

We provide a versatile formulation of Lacey's recent sparse pointwise domination technique with a local weak type estimate on a nontangential maximal function as the only hypothesis. We verify this hypothesis for sharp variational truncations of singular integrals in the case when unweighted $L^2$ estimates are available. This extends previously known sharp weighted estimates for smooth variational truncations to the case of sharp variational truncations. We also include a sparse domination result for iterated commutators of multilinear operators with BMO functions.

v3: sparse domination result extended to spaces of homogeneous type

References in corpus (7)

• On pointwise estimates involving sparse operators
• Weighted variation inequalities for differential operators and singular integrals in higher dimensions
• Sharp Reverse Hölder property for A_\infty weights on spaces of homogeneous type
• The A_2 theorem: Remarks and complements
• Three observations on commutators of Singular Integral Operators with BMO functions
• L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates
• Intrinsic square functions with arbitrary aperture

Cited by in corpus (10)

• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• Multi-scale sparse domination
• Sparse bounds for maximal rough singular integrals via the Fourier transform
• Sparse Bounds for Oscillatory and Random Singular Integrals
• $A_p$-$A_{\infty }$ estimates for multilinear maximal and sparse operators
• Intrinsic square functions with arbitrary aperture
• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• Quantitative weighted bounds for the $q$-variation of singular integrals with rough kernels
• Sparse dominations and weighted variation inequalities for singular integrals and commutators
• Sparse bounds on variational norms along monomial curves