Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains
Ciqiang Zhuo, Marc Hovemann, Winfried Sickel
TL;DR
This paper investigates the complex interpolation properties of Lizorkin-Triebel-Morrey spaces on bounded domains, revealing their relation to diamond spaces under specific parameter conditions.
Contribution
It extends the understanding of complex interpolation for Sobolev-Morrey and Lizorkin-Triebel-Morrey spaces on bounded domains, introducing new results about their interpolation scales.
Findings
Interpolation results lead to the identification of diamond spaces
Conditions on parameters determine the interpolation outcomes
Extension of known results to bounded domain settings
Abstract
In this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Differential Equations and Boundary Problems · Mathematical Analysis and Transform Methods