Geodesic
Duality in a~stability problem for some functionals arising in interpolation theory
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 207-214

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By using duality, it is shown that there exist near-minimizers for the distance functionals for the couple $(L^\infty,L^p)$, $1$, that are stable under the action of singular integral operators. 
@article{ZNSL_2018_467_a16,
     author = {A. S. Tselishchev},
     title = {Duality in a~stability problem for some functionals arising in interpolation theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--214},
     publisher = {mathdoc},
     volume = {467},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a16/}
}
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A. S. Tselishchev. Duality in a~stability problem for some functionals arising in interpolation theory. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 207-214. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a16/