The Riesz transform of codimension smaller than one and the Wolff energy /

"Fix d [greater than or equal to] 2, and s [epsilon] (d - 1, d). We characterize the non-negative locally finite non-atomic Borel measures [mu] in Rd for which the associated s-Riesz transform is bounded in L²([mu]) in terms of the Wolff energy. This extends the range of s in which the Mateu-Pr...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Jaye, Benjamin, 1984- (Author), Nazorov, Fedor (Fedya L'vovich) (Author), Reguera, Maria Carmen, 1981- (Author), Tolsa, Xavier (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, [2020]
Series:Memoirs of the American Mathematical Society, number 1293
Subjects:
Harmonic analysis.
Lipschitz spaces.
Laplacian operator.
Calderón-Zygmund operator.
Potential theory (Mathematics)
Potential theory (Physics)
Analyse harmonique.
Espaces de Lipschitz.
Laplacien.
Opérateur de Calderón-Zygmund.
Théorie du potentiel.
Análisis armónico
Potencial, Teoría del (Matemáticas)
Calderón-Zygmund operator
Harmonic analysis
Laplacian operator
Lipschitz spaces
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables {For automorphic theory, see mainly 11F30} > Harmonic analysis and PDE [See also 35-XX].
Potential theory {For probabilistic potential theory, see 60J45} > Higher-dimensional theory > Potentials and capacities, extremal length.
Online Access:Texto completo
Table of Contents:
  • The general scheme : finding a large Lipschitz oscillation coefficient
  • Upward and downward domination
  • Preliminary results regarding reflectionless measures
  • The basic energy estimates
  • Blow up I : The density drop
  • The choice of the shell
  • Blow up II : doing away with [epsilon]
  • Localization around the shell
  • The scheme
  • Suppressed kernels
  • Step I : Calderón-Zygmund theory (from a distribution to an Lp-function)
  • Step II : The smoothing operation
  • Step III : The variational argument
  • Contradiction.

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