Work

Relationship Between Limiting K ‐Spaces and J ‐Spaces in the Real Interpolation

Year: 2026

Type: article

Abstract: ABSTRACT In the paper, “Description of the ‐Spaces by Means of ‐Spaces and the Reverse Problem,” Mathematische Nachrichten 296, no. 9 (2023), 4002–4031, we have established conditions under which the limiting ‐space , involving a slowly varying function , can be described by means of the ‐space , with a convenient slowly varying function , and we have also solved the reverse problem. It has been shown that if these conditions are not satisfied, then the given problem may not have a solution. In this paper, we assume that these conditions are not satisfied. Nevertheless, our aim is to express the limiting ‐space as some limiting ‐space , and, similarly, to express the limiting ‐space as a convenient limiting ‐space . To be more precise, we show that and where and are convenient weights. Moreover, we establish equivalent norms in the above‐mentioned spaces. The obtained results are applied to get density theorems for spaces in question. As an example, we prove the density of the set in the Besov space involving the zero classical smoothness and a slowly varying smoothness . Note also that our results play important role in calculation of duals of limiting interpolation spaces and .

Source: Mathematische Nachrichten

DOI: 10.1002/mana.70159

Authors: Bohumír Opic, Manvi Grover

Institutions: Charles University, South Asian University

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,460

Funder: Grantová Agentura České Republiky