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  • Let 1 < p <= q < 1. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions.
  • Let 1 < p <= q < 1. Inspired by some results concerning characterization of weighted Hardy type inequalities, where the equivalence of four scales of integral conditions was proved, we use related ideas to find some new equivalent scales of integral conditions related to the Stieltjes transform. By applying our result to weighted inequalities for the Stieltjes transform we obtain four new scales of conditions for characterization of this inequality. We also derive a new characterization for the solvability of a Riccati type equation and show via our new results that this characterization can be done in infinite many ways via our four scales of equivalent conditions. (en)
Title
  • The weighted Stieltjes inequality and applications
  • The weighted Stieltjes inequality and applications (en)
skos:prefLabel
  • The weighted Stieltjes inequality and applications
  • The weighted Stieltjes inequality and applications (en)
skos:notation
  • RIV/67985840:_____/13:00391951!RIV14-GA0-67985840
http://linked.open...avai/riv/aktivita
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  • P(GA201/08/0383), Z(AV0Z10190503)
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  • 7
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  • 117235
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  • RIV/67985840:_____/13:00391951
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  • inequalities; Stieltjes' transform; weights (en)
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  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [2271DF43CB0B]
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  • Mathematische Nachrichten
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  • 286
http://linked.open...iv/tvurceVysledku
  • Gogatishvili, Amiran
  • Persson, L. E.
  • Kufner, Alois
http://linked.open...ain/vavai/riv/wos
  • 000318295100005
http://linked.open...n/vavai/riv/zamer
issn
  • 0025-584X
number of pages
http://bibframe.org/vocab/doi
  • 10.1002/mana.201100092
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