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<p>In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities have been obtained by several authors. Owing to sparse domination, we can treat general weights in Muckenhoupt classes. As an application, we present local and global existence results for the Hardy-Hénon parabolic equation, whose potential belonging to a Muckenhoupt class.</p>

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Two-Weight Inequality for the Heat Flow and Solvability of Hardy-Hénon Parabolic Equation

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Yohei Tsutsui

摘要

In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities have been obtained by several authors. Owing to sparse domination, we can treat general weights in Muckenhoupt classes. As an application, we present local and global existence results for the Hardy-Hénon parabolic equation, whose potential belonging to a Muckenhoupt class.