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A refinement of a Hardy type inequality for negative exponents, and sharp applications to Muckenhoupt weights on $\mathbb R$

Volume 157 / 2019

Eleftherios N. Nikolidakis, Theodoros Stavropoulos Colloquium Mathematicum 157 (2019), 295-308 MSC: Primary 26D15; Secondary 42B25. DOI: 10.4064/cm7579-8-2018 Published online: 3 June 2019


We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on $\mathbb R$. This work refines the results of Nikolidakis (2014).


  • Eleftherios N. NikolidakisDepartment of Mathematics
    University of Ioannina
    University Campus
    45110, Ioannina, Greece
  • Theodoros StavropoulosDepartment of Mathematics
    National and Kapodistrian University of Athens
    University Campus, Zografou
    15784, Athens, Greece

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