Abstract:
Firstly, sharp reiteration theorems for the K−interpolation method in limiting cases
are proved using two-sided estimates of the K−functional. As an application, sharp
mapping properties of the Riesz potential are derived in a limiting case. Secondly, we
prove optimal embeddings of the homogeneous Sobolev spaces built-up over function
spaces in R n with K−monotone and rearrangement invariant norm into another
rearrangement invariant function spaces. The investigation is based on pointwise and
integral estimates of the rearrangement or the oscillation of the rearrangement of f
in terms of the rearrangement of the derivatives of f .
