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<p>This paper deals with Hardy inequalities with additional terms. We prove new one-dimensional inequalities and using them we establish Avkhadiev-Hardy-type inequalities involving the hyperbolic radius and new inequalities for antisymmetric functions. We consider Avkhadiev-Hardy-type inequalities in simply or doubly connected plane domains of hyperbolic type. Inequalities for antisymmetric functions are considered in the 2D-case. Our results imply certain inequalities with optimal constants. The proof of these not related inequalities is based on the same one-dimensional inequalities.</p>

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Augmented Hardy Type Inequalities for Planar Domains

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Ramil Nasibullin

摘要

This paper deals with Hardy inequalities with additional terms. We prove new one-dimensional inequalities and using them we establish Avkhadiev-Hardy-type inequalities involving the hyperbolic radius and new inequalities for antisymmetric functions. We consider Avkhadiev-Hardy-type inequalities in simply or doubly connected plane domains of hyperbolic type. Inequalities for antisymmetric functions are considered in the 2D-case. Our results imply certain inequalities with optimal constants. The proof of these not related inequalities is based on the same one-dimensional inequalities.