标题： 迹和扩展定理将Besov空间与加权平均Sobolev空间联系起来 显示英文标题

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

摘要： 已知有迹定理和扩展定理，将域U中的加权Sobolev空间中的函数与边界bU上的Besov空间中的函数联系起来。我们通过修改我们的Sobolev空间，考虑Whitney球中函数的平均值，将这些定理扩展到Sobolev指数p小于一的情况。在p大于一的情况下，平均Sobolev空间在应用中也具有重要意义，因此我们也在这种情况下提供迹和扩展结果。最后，我们还为Neumann迹和扩展提供了一些可比较的结果。 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.