Geodesic
The dual of the Sobolev space of vector-valued functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 119-120

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Necessary and sufficient conditions are derived for the equality $W^\ell E(X)^\ast=W^\ell E^\prime(X^\ast)$, where $E$ is a symmetric space, $X$ a Banach space, $\ell>0$ is an integer. 
@article{ZNSL_1987_159_a10,
     author = {A. V. Bukhvalov},
     title = {The dual of the {Sobolev} space of vector-valued functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {119--120},
     publisher = {mathdoc},
     volume = {159},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a10/}
}
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A. V. Bukhvalov. The dual of the Sobolev space of vector-valued functions. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part 8, Tome 159 (1987), pp. 119-120. http://geodesic.mathdoc.fr/item/ZNSL_1987_159_a10/