具有一定混合光滑模的Besov型函数空间内的迹定理

ON TRACE THEOREMS IN A BESOV-TYPE SPACE OF MULTIVARIATE PERIODIC FUNCTIONS WITH A GIVEN MIXED MODULOUS OF SMOOTHNESS

在多元周期的Ｌｐ（１＜ｐ＜∞）空间内，对一类具有一定混合光滑模的、被赋以Ｂｅｓｏｖ型范数的线性子空间，利用Ｎｉｋｏｌｓｋｉｉ－Ｌｉｚｏｒｋｉｎ型的函数表现定理证明了嵌入定理、迹定理及其逆定理（延拓定理）。

In a class of Besov-type normed linear spaces of multivariate periodic functions with a given mixed modulous of smoothness some imbedding theorem and trace theorems are established. The main tool to get these results is a representation theorem of Besov-Nikolskii type especially established for these spaces.