Borderline weak‐type estimates for singular integrals and square functions

DOI10.1112/blms/bdv090zbMath1343.42012arXiv1505.01804OpenAlexW3102506696MaRDI QIDQ2788654

Michael T. Lacey, Guillermo Rey, Carlos Domingo-Salazar

Publication date: 22 February 2016

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01804

zbMATH Keywords

singular integralsMuckenhoupt weightssquare functionsweak-type estimates

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

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Variational characterizations of weighted Hardy spaces and weighted spaces ⋮ On \(A_p\)-\(A_\infty \) type estimates for square functions ⋮ On pointwise and weighted estimates for commutators of Calderón-Zygmund operators ⋮ Weighted theory of Toeplitz operators on the Bergman space ⋮ Endpoint entropy Fefferman-Stein bounds for commutators ⋮ Weighted weak-type inequalities for square functions ⋮ A sparse approach to mixed weak type inequalities ⋮ Vector-valued operators, optimal weighted estimates and the \(C_p\) condition ⋮ A characterization of the weighted weak type Coifman-Fefferman and Fefferman-Stein inequalities ⋮ Weak and strong $A_p$-$A_\infty $ estimates for square functions and related operators ⋮ A sparse quadratic \(T(1)\) theorem ⋮ On a counterexample related to weighted weak type estimates for singular integrals ⋮ Sharp off-diagonal weighted weak type estimates for sparse operators ⋮ Borderline weighted estimates for commutators of singular integrals ⋮ Stein's square function \(G_\alpha \) and sparse operators ⋮ Sparse and weighted estimates for generalized Hörmander operators and commutators ⋮ Borderline weak-type estimates for sparse bilinear forms involving \(A_\infty\) maximal functions ⋮ On the embedding of 𝐴₁ into 𝐴_{∞} ⋮ Weighted norm inequalities for rough singular integral operators ⋮ Borderline Weighted Estimates for Commutators of Fractional Integrals ⋮ A weighted endpoint weak-type estimate for multilinear Calderón-Zygmund operators

Cites Work

• Sharp weighted bounds involving \(A_\infty\)
• On Muckenhoupt-Wheeden conjecture
• Weights, extrapolation and the theory of Rubio de Francia.
• Extrapolation of weights revisited: new proofs and sharp bounds
• Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals
• The intrinsic square function
• \(A_1\) bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden
• The \(L(\log L)^\epsilon\) endpoint estimate for maximal singular integral operators
• The Hilbert transform does not map \(L^1(M\omega)\) to \(L^{1,\infty}(\omega)\)
• Muckenhoupt–Wheeden conjectures in higher dimensions
• Multiparameter operators and sharp weighted inequalities
• Factorization Theory and A P Weights
• CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS
• Sharp A1 Bounds for Calderón-Zygmund Operators and the Relationship with a Problem of Muckenhoupt and Wheeden
• Factorization and extrapolation of weights
• Weighted norm inequalities for maximal functions and singular integrals
• Weighted Norm Inequalities for Singular Integral Operators
• Some Maximal Inequalities

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