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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 \(p,q\geq 1,1/p+\alpha /n,1/q+\beta /n,1/r+\gamma /n>0\).

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
Full Text: DOI
[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
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