Description of traces of the functions whose derivatives are bounded with certain weights (Q1060390)

The authors obtain an imbedding theorem for the class \(L^{r,s}_{\xi,\phi}\) of functions whose generalized derivatives of order r with respect to y and of order s with respect to x are bounded with some weights \(\xi\) (y) and \(\phi\) (y). It is shown that for some conditions on the weight functions the trace of these functions (their limit for \(y\to +0)\) are in the generalized Lipschitz space \(\Lambda^ s_{\omega}\) with the modulus of smoothness \(\omega\) which can be explicitely determined.