## 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.

### MSC:

 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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