On the support of Zygmund measures

Authors

  • Laia Weisz Font Laia Weisz Font Universitat Autònoma de Barcelona (UAB)

Keywords:

Zygmund measures, Kaufman's Theorem, log-porosity.

Abstract

We analyse the compact sets that are the support of Zygmund measures, of which no characterisation is known. We introduce the concept of log-porosity which provides a sufficient condition that guarantees that a compact cannot be the support of a Zygmund measure. This result does not derive from the results of Makarov and Kaufman. We introduce the concept of Zygmund capacity of a compact and propose a characterisation of the supports of Zygmund measures in terms of this capacity. We prove that the compact sets for which the limit of this capacity is zero cannot be the support of Zygmund measures.

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How to Cite

Weisz Font, L. (2022). On the support of Zygmund measures. Reports@SCM, 7(1), 1–12. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/150089

Issue

Vol. 7 No. 1 (2022)

Section

Articles

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