The Cauchy integral operator over general paths

Ziel

The Cauchy integral operator is the prototype example of a singular integral operator in the complex variable setting
and the fundamental object to be understood in the problem of characterization of removable sets for bounded analytic functions. By many different reasons, the study of this operator has always been confined to the setting of Lipschitz paths.
However, recent developments in a relatively new technique called time-frequence analysis suggests that the theory may be extended to more general paths.
Therefore, we propose the study of boundedness of Cauchy integral operator defined over paths that can be rougher than Lipschitz. We are particularly interested in the case when the derivative of the function defining the path belongs to a particular Lebesgue space.
For such purpose, we propose the use of time-frequency analysis and the use of variation norms.
Once boundedness in Lebesgue spaces is obtained, we will be able to establish new lower bounds for the analytic capacity of a compact set, which which is a quantitative measurement of the possibility of being removable.

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UNIVERSITAT AUTONOMA DE BARCELONA

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€ 45 000,00

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EDIF A CAMPUS DE LA UAB BELLATERRA CERDANYOLA V
08193 Cerdanyola Del Valles
Spanien

Region

Este Cataluña Barcelona

Aktivitätstyp

Higher or Secondary Education Establishments

Kontakt Verwaltung

Queralt Gonzalez Matos (Ms.)

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