Unboundedness of potential dependent Riesz transforms for totally irregular measures

DOI10.1016/J.JMAA.2020.124570zbMath1477.42013arXiv2001.05526OpenAlexW3083710108MaRDI QIDQ2226343

Julian Bailey, Andrew J. Morris, Maria Carmen Reguera

Publication date: 12 February 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.05526

zbMATH Keywords

Schrödinger operatorRiesz transformstotally irregular measure

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fundamental solutions to PDEs (35A08) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Schrödinger operator, Schrödinger equation (35J10) Length, area, volume, other geometric measure theory (28A75) Harmonic analysis and PDEs (42B37)

Related Items (4)

Gradient estimates and the fundamental solution for higher-order elliptic systems with lower-order terms ⋮ \(L^2\)-boundedness of gradients of single layer potentials for elliptic operators with coefficients of Dini mean oscillation-type ⋮ Weights of exponential growth and decay for Schrödinger-type operators ⋮ Gradient of the single layer potential and quantitative rectifiability for general Radon measures

Cites Work

• Unnamed Item
• On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
• The \(s\)-Riesz transform of an \(s\)-dimensional measure in \(\mathbb R^2\) is unbounded for \(1<s<2\)
• The Green function for uniformly elliptic equations
• Removable sets for Lipschitz harmonic functions in the plane
• Elliptic partial differential equations of second order
• Fundamental matrices and Green matrices for non-homogeneous elliptic systems
• Failure of \(L^2\) boundedness of gradients of single layer potentials for measures with zero low density
• On fundamental solutions of generalized Schrödinger operators
• \(L^ p\) estimates for Schrödinger operators with certain potentials
• The Cauchy integral, analytic capacity, and uniform rectifiability
• Calderón-Zygmund capacities and Wolff potentials on Cantor sets
• The Green function estimates for strongly elliptic systems of second order
• Riesz transforms of non-integer homogeneity on uniformly disconnected sets
• Layer potential methods for elliptic homogenization problems
• The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
• Modern Fourier Analysis
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• The Capacity Associated to Signed Riesz Kernels, and Wolff Potentials
• Riesz transforms and harmonic Lip1-capacity in Cantor sets
• Exponential decay estimates for fundamental solutions of Schrödinger-type operators

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