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<p>In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan–Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance. Secondly, we examine the stability of both critical and subcriwtical cases of the Hardy inequality. Lastly, we establish two weighted Hardy-type inequalities where singularities appear at the origin as well as the boundary, and we discuss their implications for higher-order operators. Our results improve upon previous findings and also present new higher-order versions of these inequalities as additional outcomes.</p>

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Critical, stability and higher-order analysis for Hardy type inequalities on Cartan–Hadamard manifolds

  • 期刊论文

  • 发表日期：

    2025年9月16日

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  • Prasun Roychowdhury,
  • Durvudkhan Suragan,
  • Nurgissa Yessirkegenov

摘要

In this paper, we focus on three main objectives related to Hardy-type inequalities on Cartan–Hadamard manifolds. Firstly, we explore critical Hardy-type inequalities that contain logarithmic terms, highlighting their significance. Secondly, we examine the stability of both critical and subcriwtical cases of the Hardy inequality. Lastly, we establish two weighted Hardy-type inequalities where singularities appear at the origin as well as the boundary, and we discuss their implications for higher-order operators. Our results improve upon previous findings and also present new higher-order versions of these inequalities as additional outcomes.