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Isomorphism Between Sobolev Spaces and Bessel Potential Spaces in the Setting of Wiener Amalgam Spaces

Commun. Math. Anal.
Volume 16, Number 2 (2014), 57 - 73

Isomorphism Between Sobolev Spaces and Bessel Potential Spaces in the Setting of Wiener Amalgam Spaces

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Abstract

A classical result due to A. P. Calder\'{o}n states that Bessel potential spaces and Sobolev spaces defined on the same Lebesgue space and of the same integer order are isomorphic. We show that this result remains true when we replace Lebesgue spaces by some particular subspaces of Wiener amalgam space.