Almost sharp descriptions of traces of Sobolev spaces on compacta (Q2063693)

In this short communication the author takes into account the concepts of $d$-Hausdorff measure \(H^d\), the $d$-Hausdorff content \(H^d_\infty\), dyadic Hausdorff content, and makes use of some far-reaching generalization of the Calderón maximal function. Then, as the main result a theorem is presented where the inclusions of trace spaces and the inequalities related to a suitable quotient space by the subspace of zeros of the corresponding seminorm are involved. The inclusions and the inequalities shed light on the origin of the term almost sharp description of the trace.