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<p>In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt’s class, and the initial data is in weighted Besov spaces with variable order.</p>

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A Regularity Theory for an Initial Value Problem with a Time-measurable Pseudo-differential Operator in a Weighted \(L_p\)-space

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Jae-Hwan Choi,
  • Ildoo Kim,
  • Jin Bong Lee

摘要

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt’s class, and the initial data is in weighted Besov spaces with variable order.