Measures that define a compact cauchy transform

Carmelo Puliatti, Svitlana Mayboroda

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this work is to provide a geometric characterization of the positive Radon measures µ with compact support on the plane such that the associated Cauchy transform defines a compact operator from L 2 (µ) to L 2 (µ). It turns out that a crucial role is played by the density of the measure and by its Menger curvature.

Original languageEnglish (US)
Pages (from-to)2069-2080
Number of pages12
JournalProceedings of the American Mathematical Society
Volume147
Issue number5
DOIs
StatePublished - May 2019

Bibliographical note

Funding Information:
The author wants to express his gratitude to the anonymous referee for a careful read of the paper and helpful comments. He is also thankful to his advisors, Xavier Tolsa and Joan Verdera. The author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the María de Maeztu Programme for Units of Excellence in R&D (MDM- 2014-0445). Partiallly supported by MTM-2016-77635-P, MDM-2014-044 (MICINN, Spain), 2017- SGR-395 (Catalonia), and Marie Curie ITN MAnET (FP7-607647).

Funding Information:
Received by the editors March 1, 2018, and, in revised form, July 20, 2018. 2010 Mathematics Subject Classification. Primary 42B20, 28A80. The author acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445). Partiallly supported by MTM-2016-77635-P, MDM-2014-044 (MICINN, Spain), 2017-SGR-395 (Catalonia), and Marie Curie ITN MAnET (FP7-607647).

Publisher Copyright:
© 2019 American Mathematical Society.

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