On some weighted norm inequalities for Littlewood-Paley operators

zbMath1177.42016MaRDI QIDQ733341

Andrei K. Lerner

Publication date: 15 October 2009

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ijm/1248355356

zbMATH Keywords

maximal operators\(A_p\) weightsLittlewood-Paley operatorsweighted \(L^p\) boundedness

Mathematics Subject Classification ID

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

Related Items

Weak and strong type estimates for maximal truncations of Calderón-Zygmund operators on \(A_p\) weighted spaces ⋮ Haar multipliers meet Bellman functions ⋮ The sharp weighted maximal inequalities for noncommutative martingales ⋮ Martingale Hardy-Lorentz spaces -- a unified approach ⋮ Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals ⋮ Dual spaces and inequalities of new weak martingale Hardy spaces ⋮ Mixed estimates for singular integrals on weighted Hardy spaces ⋮ A sparse quadratic \(T(1)\) theorem ⋮ Sharp weighted estimates for classical operators ⋮ Generalized homogeneous Littlewood-Paley \(g\)-function on some function spaces ⋮ Bi-parameter Littlewood-Paley operators with upper doubling measures ⋮ Bounds of singular integrals on weighted Hardy spaces and discrete Littlewood-Paley analysis ⋮ Quantitative boundedness of Littlewood-Paley functions on weighted Lebesgue spaces in the Schrödinger setting ⋮ Multilinear Littlewood-Paley-Stein operators on non-homogeneous spaces ⋮ Weighted 𝐿² inequalities for square functions

Cites Work

• Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces
• On some sharp weighted norm inequalities
• Some weighted norm inequalities concerning the Schrödinger operators
• On some pointwise inequalities.
• A sharp estimate on the norm of the martingale transform
• An estimate for weighted Hilbert transform via square functions
• Multiparameter operators and sharp weighted inequalities
• Chanillo-Wheeden Inequalities for 0 < p ⩽ 1
• Erratum to "Weighted Norm Inequalities for the Continuous Square Function"
• Another Characterization of BMO
• Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities
• A sharp estimate on the norm of the continuous square function
• Weighted norm estimates for gradients of half-space extensions
• The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic
• The sharp weighted bound for the Riesz transforms
• Weighted Norm Inequalities for the Hardy Maximal Function
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