Clarkson's inequalities, Besov spaces and Triebel-Sobolev spaces
Carkson's inequalities in \(L_ p\) are generalizations of the parallelogram law in \(L_ 2\). They also show that \(L_ p\) is uniformly convex for p greater than one. The present note shows that the same inequalities hold in some Besov spaces and Triebel-Sobolev spaces. The proof is based on the computation of the type or cotype constants of certain of those spaces. The Clarkson inequalities then follow immediately provided a suitable \(L_ r\)-norm is chosen by the definition of the Radamacher type or cotype.
computation of the type or cotype constants
scientific article; zbMATH DE number 4084332