Work

Kondratiev spaces of fractional smoothness via refined localization spaces

Year: 2026

Type: article

Abstract: In this paper, we introduce Kondratiev spaces of fractional smoothness based on their close relation to refined localization spaces. Moreover, we investigate relations to other approaches leading to extensions of the scale of Kondratiev spaces with integer order of smoothness, based on complex interpolation, and give further results for complex interpolation of those function spaces. The results are first established on complements of arbitrary closed Lebesgue null sets and then transferred to domains of polyhedral type. Finally, as an application, we will study Sobolev-type embeddings.

Source: Zeitschrift für Analysis und ihre Anwendungen

DOI: 10.4171/zaa/1845

Authors: Markus Hansen, Cornelia Schneider

Institutions: Philipps University of Marburg, Friedrich-Alexander-Universität Erlangen-Nürnberg

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: FP7 Ideas: European Research Council

Award: High-Dimensional Sparse Optimal Control