Duals of limiting interpolation spaces
Manvi Grover, Bohum\'ir Opic

TL;DR
This paper determines the dual spaces of certain limiting real interpolation spaces involving Banach space couples, extending classical results by Lions and Peetre to more general limiting cases.
Contribution
It establishes the duality of limiting real interpolation $K$- and $J$-spaces with slowly varying functions, generalizing classical duality results.
Findings
Duals of limiting interpolation spaces are characterized.
Extends classical duality results to limiting cases.
Provides a framework for duality in more general interpolation settings.
Abstract
The aim of the paper is to establish duals of the limiting real interpolation - and -spaces and , where is a compatible couple of Banach spaces, , is a slowly varying function on the interval , and the symbols and stand for the Peetre - and -functionals. In the case of the classical real interpolation method , where and , this problem was solved by Lions and Peetre.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Advanced Banach Space Theory · Approximation Theory and Sequence Spaces
