×

zbMATH — the first resource for mathematics

Interpolation inequalities with weights. (English) Zbl 0635.46032
Summary: We use elementary methods to prove a sufficient and necessary condition for Sobolev interpolation inequalities with weight \[ | | x|^{\gamma}D\quad ju|_ r\leq C| | x|^{\alpha}D\quad mu| \quad a_{L\quad p}| | x|^{\beta}u|_{L\quad q}^{1-a}, \] where p, \(\alpha\), q, \(\beta\), \(\gamma\), r are real numbers, and \(p,q\geq 1,1/p+\alpha /n,1/q+\beta /n,1/r+\gamma /n>0\).

MSC:
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
46M35 Abstract interpolation of topological vector spaces
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Caffarelli L., Compositio Math. 53 pp 259– (1984)
[2] Nirenberg L., Ann. di Pisa 9 pp 1515– (1962)
[3] Friedman A., Partial different ialequations
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.