Weighted inequalities involving two hardy operators with applications to embeddings of function spaces

María Carro, Amiran Gogatishvili, Joaquim Martín, Luboš Pick

Research output: Contribution to journalArticleResearchpeer-review

30 Citations (Scopus)

Abstract

We find necessary and sufficient conditions for the two-operator weighted inequality (Equation Presented). We use this inequality to study embedding properties between the function spaces Sp(u) equipped with the norm (Equation Presented) and the classical Lorentz spaces Λp(v) and Γq(w). Moreover, we solve the only missing open case of the embedding Λp (v) → Γq(W) where 0 ≪ q ≪ p ≤. © Copyright by Theta, 2008.
Original languageEnglish
Pages (from-to)309-332
JournalJournal of Operator Theory
Volume59
Issue number2
Publication statusPublished - 1 Jan 2008

Keywords

  • Average operator
  • Classical lorentz spaces
  • Dual average operator
  • Embeddings
  • Spaces S (w) p
  • Two-operator weighted inequality
  • Weighted inequalities

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