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A note on the Muckenhoupt class $A_1(\mathbb R)$

Eleftherios N. Nikolidakis, Andreas G. Tolias Bulletin Polish Acad. Sci. Math. MSC: Primary 42B25 DOI: 10.4064/ba260310-23-6 Published online: 14 July 2026

Abstract

We provide a direct proof of the best possible reverse Hölder inequality satisfied by every $A_1$-weight defined on $({0,1})$ with $A_1$-constant equal to $c \gt 1$.

Authors

  • Eleftherios N. NikolidakisDepartment of Mathematics
    University of Ioannina
    Ioannina 45110, Greece
    e-mail
  • Andreas G. ToliasDepartment of Mathematics
    University of Ioannina
    Ioannina 45110, Greece
    e-mail

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