Dyadic harmonic analysis beyond doubling measures

DOI10.1016/j.aim.2014.08.001zbMath1304.42041arXiv1211.6291OpenAlexW1986234073MaRDI QIDQ462282

Luis Daniel López-Sánchez, Javier Parcet, José Maria Martell

Publication date: 20 October 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.6291

zbMATH Keywords

Calderón-Zygmund decompositionnon-doubling measuresgeneralized Haar systemsdyadic cubesdyadic Hilbert transformdyadic paraproductsHaar shift operators

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items (12)

Entropy conditions in two weight inequalities for singular integral operators ⋮ Spectral multipliers in group algebras and noncommutative Calderón-Zygmund theory ⋮ Sparse domination for the lattice Hardy–Littlewood maximal operator ⋮ Sparse domination results for compactness on weighted spaces ⋮ Weighted martingale multipliers in the non-homogeneous setting and outer measure spaces ⋮ Nonlocal Schrödinger equations in metric measure spaces ⋮ Products and commutators of martingales in \(H_1\) and BMO ⋮ Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution ⋮ Nondoubling Calderón-Zygmund theory: a dyadic approach ⋮ Haar bases on quasi-metric measure spaces, and dyadic structure theorems for function spaces on product spaces of homogeneous type ⋮ Operator-valued dyadic harmonic analysis beyond doubling measures ⋮ Two-weight inequality for operator-valued positive dyadic operators by parallel stopping cubes

Cites Work

• Unnamed Item
• Unnamed Item
• The sharp weighted bound for general Calderón-Zygmund operators
• Weighted inequalities for multivariable dyadic paraproducts
• Weights, extrapolation and the theory of Rubio de Francia.
• Sharp weighted estimates for classical operators
• Linear bound for the dyadic paraproduct on weighted Lebesgue space \(L_2(w)\)
• Clifford wavelets, singular integrals, and Hardy spaces
• A new class of unbalanced Haar wavelets that form an unconditional basis for \(L_ p\) on general measure spaces
• Sharp estimate of the Ahlfors-Beurling operator via averaging martingale transforms
• A sharp estimate on the norm of the martingale transform
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular
• Paraproducts and the exponential-square class
• Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces
• \(L^2\)-boundedness of the Cauchy integral operator for continuous measures
• The vector-valued nonhomogeneous Tb Theorem
• Martingale Transforms
• Estimates for Operator Norms on Weighted Spaces and Reverse Jensen Inequalities
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol
• 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
• A Decomposition for $L^1$-Bounded Martingales

This page was built for publication: Dyadic harmonic analysis beyond doubling measures