We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ℝⁿ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-1,
author = {Irshaad Ahmed and Georgi Eremiev Karadzhov},
title = {Optimal embeddings of generalized homogeneous Sobolev spaces},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {1-20},
zbl = {1219.46030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-1}
}
Irshaad Ahmed; Georgi Eremiev Karadzhov. Optimal embeddings of generalized homogeneous Sobolev spaces. Colloquium Mathematicae, Tome 122 (2011) pp. 1-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm123-1-1/