Local growth envelopes of spaces of generalized smoothness: The subcritical case. (English) Zbl 1070.46020

Caetano, António M.; Moura, Susana D.

Math. Nachr. 273, 43-57 (2004).

Summary: The concept of local growth envelope (\(\mathcal E_{\text{LG}}A, u\)) of a quasi-normed function space \(A\) is applied to spaces of generalized smoothness \(B^{(s,\Psi)}_{pq} (\mathbb R^n)\) and \(F^{(s,\Psi)}_{pq} (\mathbb R^n)\) and it is shown that the influence of the function \(\Psi\), which is a fine tuning of the main smoothness parameter \(s\), is strong enough in order to show up in the corresponding growth envelopes.

MSC:

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

function spaces of generalized smoothness; local growth envelopes; essential unboundedness