发表机构
Cellular Products Research and Development; Antalya Bilim University（细胞产品研究与开发; 安塔利亚科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了向量值Morrey时间控制演化类的精确迹为弱实插值空间，证明其与经典L^p理论本质不同，并在插值参数上尖锐，为Morrey型极大正则性演化方程提供了迹框架。
AI 中文摘要
迹空间决定了哪些初值与一个演化类相容。我们确定了由时间方向上的向量值Morrey控制所生成的精确迹，并证明其本质上不同于经典的$L^p$理论。对于Banach偶$X_1\hookrightarrow X_0$，自然Morrey演化类的迹是弱实插值空间$(X_0,X_1)_{\theta,\infty}$，其中$\theta=1-(1-\lambda)/p$。该空间的每个元素都可通过一个有界延拓算子作为迹出现。结果在两个插值参数上都是尖锐的：一般而言，光滑性指数不能增大，精细指标$\infty$不能被任何有限指标替换。因此，Morrey控制改变了精确迹机制，而不仅仅是加强了一个可积性估计。在极限端点，有界平均振动（BMO）控制产生有限指标插值迹以及一个对数模连续性。该结果分离出了与局部、尺度敏感的时间正则性自然相关的精确初值空间，并为具有Morrey型极大正则性的演化方程提供了一个迹框架。关键词：Morrey空间，迹空间，实插值，演化方程，有界平均振动。
英文摘要
Trace spaces determine exactly which initial values are compatible with an evolution class. We identify the exact trace generated by vector-valued Morrey control in time and show that it differs essentially from the classical $L^p$ theory. For a Banach couple $X_1\hookrightarrow X_0$, the trace of the natural Morrey evolution class is the weak real-interpolation space $(X_0,X_1)_{θ,\infty}$, where $θ=1-(1-λ)/p$. Every element of this space occurs as a trace through a bounded extension operator. The result is sharp in both interpolation parameters: in general the smoothness exponent cannot be increased and the fine index $\infty$ cannot be replaced by any finite index. Thus Morrey control changes the exact trace mechanism rather than merely strengthening an integrability estimate. At the limiting endpoint, bounded mean oscillation (BMO) control yields finite-index interpolation traces together with a logarithmic modulus of continuity. The result isolates the precise initial-data space naturally associated with local, scale-sensitive time regularity and provides a trace framework suited to evolution equations with Morrey-type maximal regularity. \keywords{Morrey spaces \and trace spaces \and real interpolation \and evolution equations \and bounded mean oscillation}
