标题： 关于Besov空间与加权平均Sobolev空间相关的跟踪和扩展定理 显示英文标题

标题： Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces

摘要： 已知有定理可以将区域 \( U \) 中加权Sobolev空间中的函数与边界 \( bU \) 上的Besov空间中的函数联系起来。我们通过修改Sobolev空间以考虑Whitney球内函数的平均值，将这些定理扩展到Sobolev指数 \( p \) 小于一的情况。当 \( p > 1 \) 时，平均Sobolev空间在应用中也有兴趣，因此我们也提供了在这种情况下迹和延拓的结果。最后，我们还提供了一些关于Neumann迹和延拓的可比结果。 显示英文摘要

摘要： There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. We extend these theorems to the case where the Sobolev exponent p is less than one by modifying our Sobolev spaces to consider averages of functions in Whitney balls. Averaged Sobolev spaces are also of interest in the applications in the case where p>1, and so we also provide trace and extension results in that case. Finally, we provide some comparable results for Neumann traces and extensions.