Description 
1 online resource 
Series 
Memoirs of the American Mathematical Society, 00659266 ; number 1293 
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 : CalderónZygmund theory (from a distribution to an Lpfunction)  Step II : The smoothing operation  Step III : The variational argument  Contradiction 
Summary 
"Fix d [greater than or equal to] 2, and s [epsilon] (d  1, d). We characterize the nonnegative locally finite nonatomic Borel measures [mu] in Rd for which the associated sRiesz transform is bounded in L²([mu]) in terms of the Wolff energy. This extends the range of s in which the MateuPratVerdera characterization of measures with bounded sRiesz transform is known. As an application, we give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator ( [delta])[infinity]/2, [infinity] [epsilon] (1, 2), in terms of a wellknown capacity from nonlinear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions" Provided by publisher 
Notes 
"Forthcoming, volume 266, number 1293." 
Bibliography 
Includes bibliographical references 
Notes 
Print version record 
Subject 
CalderónZygmund operator.


Harmonic analysis.


Laplacian operator.


Lipschitz spaces.


Potential theory (Mathematics)


CalderónZygmund operator


Harmonic analysis on Euclidean spaces  Harmonic analysis in several variables {For automorphic theory, see mainly 11F30}  Harmonic analysis and PDE [See also 35XX].


Harmonic analysis


Laplacian operator


Lipschitz spaces


Potential theory (Mathematics)


Potential theory {For probabilistic potential theory, see 60J45}  Higherdimensional theory  Potentials and capacities, extremal length.

Form 
Electronic book

Author 
Nazorov, Fedor (Fedya L'vovich), author.


Reguera, Maria Carmen, 1981 author.


Tolsa, Xavier, author.

ISBN 
1470462494 

9781470462499 
