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<p>The classical Gagliardo–Nirenberg inequality, a fundamental result in interpolation theory, traditionally involves Lebesgue norms of functions and their derivatives. We extend this inequality by introducing an interpolation lemma that bridges Lebesgue and Hölder spaces, replacing conventional Sobolev norms with appropriate Hölder norms. This extension not only broadens the range of admissible parameters but also establishes a unified framework for inequalities in Sobolev and Hölder spaces, offering new insights and applications.</p>

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Gagliardo–Nirenberg Inequality with Hölder Norms

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Mengxia Dong

摘要

The classical Gagliardo–Nirenberg inequality, a fundamental result in interpolation theory, traditionally involves Lebesgue norms of functions and their derivatives. We extend this inequality by introducing an interpolation lemma that bridges Lebesgue and Hölder spaces, replacing conventional Sobolev norms with appropriate Hölder norms. This extension not only broadens the range of admissible parameters but also establishes a unified framework for inequalities in Sobolev and Hölder spaces, offering new insights and applications.