The converse of Fatou's theorem for Zygmund measures

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5 Citations (Scopus)

Abstract

The converse of Fatou's theorem is true for positive measures but not for arbitrary measures. We prove that the converse holds for Zygmund (smooth) measures, being this result sharp in some sense. We also give an application to differentiation of positive singular measures in the little Zygmund class.
Original languageEnglish
Pages (from-to)207-222
JournalPacific Journal of Mathematics
Volume191
Issue number2
DOIs
Publication statusPublished - 1 Jan 1999

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