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A general family of interpolation methods is introduced which includes, as special cases, the real and complex methods and also the so-called AE or G 1 and G 2 methods defined by Peetre and Gustavsson-Peetre. Derivation operators O and translation operators R are introduced for all methods of this family. A theorem is proved about

No abstract

We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations.

We present an elementary unified and self-contained proof of sharp Sobolev embedding theorems. We introduce a new function space and use it to improve the limiting Sobolev embedding theorem due to Brézis and Wainger.