Local growth envelopes of spaces of generalized smoothness: the critical case

Abstract

Abstract. 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, Ψ) in the critical case s = n/p , where s stands for the main smoothness, Ψ is a perturbation and p stands for integrability. The expression obtained for the behaviour of the local growth envelope functions (which, as expected, depends on Ψ ) shows the ability to be generalized to a form unifying both critical ( s = n/p ) and subcritical ( s < n/p ) cases. (2000): 46E35. Mathematics subject classification

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