\(H\)-distributions with unbounded multipliers
The aim of the paper is to investigate \(H\)-distributions for weakly convergent sequences in certain dual pairs of Bessel potential spaces using unbounded multipliers, with finite regularity, as test functions. As a key step, the authors previously discussed the compactness, on appropriate Bessel potential spaces, of the commutator between a multiplication operator and a Fourier multiplier with unbounded symbol of finite regularity [Mediterr. J. Math. 13, No. 5, 3499--3512 (2016; Zbl 1367.46035)]. The obtained results are used to discuss the strong convergence of sequences of approximated solutions of a certain class of differential equations.
scientific article; zbMATH DE number 6939199
scientific article