Counterexamples to some pointwise estimates of the maximal Cauchy transform in terms of the Cauchy transform
Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form T _*f\lesssim M(Tf) or T _*f\lesssim M^2(Tf) for certain singular integral operators T, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for th...
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| Format: | master thesis |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:102070 |
| Online Access: | https://ddd.uab.cat/record/102070 |
| Access Level: | Open access |
| Keyword: | Cauchy, Transformació de Operadors, Teoria dels Desigualtats (Matemàtica) Grafs, Teoria dels |
| Summary: | Motivated by the work of Mateu, Orobitg, Pérez and Verdera, who proved inequalities of the form T _*f\lesssim M(Tf) or T _*f\lesssim M^2(Tf) for certain singular integral operators T, such as the Hilbert or the Beurling transforms, we study the possibility of establishing this type of control for the Cauchy transform along a Lipschitz graph. We show that this is not possible in general, and we give a partial positive result when the graph is substituted by a Jordan curve. |
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