Direct and converse imbedding theorems for seminormed spaces (Q1812847)

The author considers the space of functions with the seminorm: \[ \sum_{|\beta|= r}\Biggl\{ \int_{x_ n> 0} | x^ \alpha_ n D^ \beta f(x)|^ p dx\Biggr\}^{1/p},\qquad 1\leq p\leq \infty, \] where \(\alpha\) is a real number. She proves trace embedding theorems for such spaces.