Displaying similar documents to “An interpolation inequality involving Hölder norms.”

Sharp embeddings of Besov spaces with logarithmic smoothness.

Petr Gurka, Bohumir Opic (2005)

Revista Matemática Complutense


We prove sharp embeddings of Besov spaces B with the classical smoothness σ and a logarithmic smoothness α into Lorentz-Zygmund spaces. Our results extend those with α = 0, which have been proved by D. E. Edmunds and H. Triebel. On page 88 of their paper (Math. Nachr. 207 (1999), 79-92) they have written: ?Nevertheless a direct proof, avoiding the machinery of function spaces, would be desirable.? In our paper we give such a proof even in a more general context. We cover...

Local interpolation by a quadratic Lagrange finite element in 1D

Josef Dalík (2006)

Archivum Mathematicum


We analyse the error of interpolation of functions from the space H 3 ( a , c ) in the nodes a < b < c of a regular quadratic Lagrange finite element in 1D by interpolants from the local function space of this finite element. We show that the order of the error depends on the way in which the mutual positions of nodes a , b , c change as the length of interval [ a , c ] approaches zero.