May the Cauchy transform of a non-trivial finite measure vanish on the support of the measure?
Tolsa, Xavier, Verdera, Joan (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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Tolsa, Xavier, Verdera, Joan (2006)
Annales Academiae Scientiarum Fennicae. Mathematica
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Cheung, Wing-Sum (2001)
International Journal of Mathematics and Mathematical Sciences
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Kinnunen, Juha, Martio, Olli (2003)
Annales Academiae Scientiarum Fennicae. Mathematica
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Dorosiewicz, Slawomir (2001)
International Journal of Mathematics and Mathematical Sciences
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Rooin, J. (2005)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Shiga, Tokuzo, Tanaka, Hiroshi (2006)
Electronic Journal of Probability [electronic only]
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Szymon Głąb, Filip Strobin (2013)
Czechoslovak Mathematical Journal
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Jachymski showed that the set is either a meager subset of or is equal to . In the paper we generalize this result by considering more general spaces than , namely , the space of all continuous functions which vanish at infinity, and , the space of all continuous bounded functions. Moreover, we replace the meagerness by -porosity.
Kisil, Vladimir V. (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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