Capacities associated with scalar signed riesz kernels, and analytic capacity

Joan Mateu; Laura Prat; Joan Verdera

doi:10.1512/iumj.2011.60.437

Capacities associated with scalar signed riesz kernels, and analytic capacity

Joan Mateu, Laura Prat, Joan Verdera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

Analytic capacity is associated with the Cauchy kernel 1/z and the space L∞. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and L∞. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to Rn, n ≥ 3, involving the vector-valued Riesz kernel of homogeneity -1 and n - 1 of its components.

Original language	English
Pages (from-to)	1319-1361
Journal	Indiana University Mathematics Journal
Volume	60
Issue number	4
DOIs	https://doi.org/10.1512/iumj.2011.60.437
Publication status	Published - 1 Dec 2011

Keywords

Analytic capacity
Linear growth. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 42B20
Scalar signed Riesz kernels

Access to Document

10.1512/iumj.2011.60.437

Fingerprint Dive into the research topics of 'Capacities associated with scalar signed riesz kernels, and analytic capacity'. Together they form a unique fingerprint.

Cite this

@article{d4204c2e089c48648faa6b6ec55f637c,

title = "Capacities associated with scalar signed riesz kernels, and analytic capacity",

abstract = "Analytic capacity is associated with the Cauchy kernel 1/z and the space L∞. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and L∞. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to Rn, n ≥ 3, involving the vector-valued Riesz kernel of homogeneity -1 and n - 1 of its components.",

keywords = "Analytic capacity, Linear growth. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 42B20, Scalar signed Riesz kernels",

author = "Joan Mateu and Laura Prat and Joan Verdera",

year = "2011",

month = dec,

day = "1",

doi = "10.1512/iumj.2011.60.437",

language = "English",

volume = "60",

pages = "1319--1361",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Indiana University",

number = "4",

}

TY - JOUR

T1 - Capacities associated with scalar signed riesz kernels, and analytic capacity

AU - Mateu, Joan

AU - Prat, Laura

AU - Verdera, Joan

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Analytic capacity is associated with the Cauchy kernel 1/z and the space L∞. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and L∞. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to Rn, n ≥ 3, involving the vector-valued Riesz kernel of homogeneity -1 and n - 1 of its components.

AB - Analytic capacity is associated with the Cauchy kernel 1/z and the space L∞. One has likewise capacities associated with the real and imaginary parts of the Cauchy kernel and L∞. Striking results of Tolsa and a simple remark show that these three capacities are comparable. We present an extension of this fact to Rn, n ≥ 3, involving the vector-valued Riesz kernel of homogeneity -1 and n - 1 of its components.

KW - Analytic capacity

KW - Linear growth. 2010 MATHEMATICS SUBJECT CLASSIFICATION: 42B20

KW - Scalar signed Riesz kernels

U2 - 10.1512/iumj.2011.60.437

DO - 10.1512/iumj.2011.60.437

M3 - Article

VL - 60

SP - 1319

EP - 1361

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 4

ER -