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Local growth envelopes of spaces of generalized smoothness: the critical case. (English) Zbl 1076.46025
The concept of local growth envelope of a quasi-normed function space is applied to the spaces of Besov and Triebel-Lizorkin type of generalized smoothness \((s,\Psi)\) in the critical case \(s=n/p\), where \(s\) stands for the main smoothness, \(\Psi\) is a perturbation and \(p\) stands for integrability. The expression obtained for the behaviour of the local growth envelope functions shows the possibility to be generalized to a form unifying both the critical \((s=n/p)\) and the subcritical \((s<n/p)\) case.

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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