Optimal embeddings of generalized homogeneous Sobolev spaces
Volume 123 / 2011
Colloquium Mathematicum 123 (2011), 1-20
MSC: Primary 46E35; Secondary 46E30
DOI: 10.4064/cm123-1-1
Abstract
We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ${\mathbb R}^n$ with $K$-monotone and rearrangement invariant norm into other 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 $f$.
