  It is well-known that the embedding of the Sobolev space of weakly
differentiable functions into H\"{o}lder spaces holds if the integrability
exponent is higher than the space dimension. In this paper, the embedding of
the Sobolev functions into the H\"{o}lder spaces is expressed in terms of the
minimal weak differentiability requirement independent of the integrability
exponent. The proof is based on the generalization of the Newton-Leibniz
formula to the $n$-dimensional rectangle and inductive application of the
Sobolev trace embedding results. The method is applied to prove the embedding
of the Sobolev spaces with dominating mixed smoothness into H\"{o}lder spaces.
