DUAL SPACES OF ANISOTROPIC MIXED-NORM HARDY SPACES

Let a := (a1,..., a(n)) is an element of [1, infinity)(n), P := (p(1),...,p(n)) is an element of (0, infinity)(n) and H-a(p)(R-n) be the anisotropic mixed-norm Hardy space associated with a, defined via the non-tangential grand maximal function. In this article, the authors give the dual space of H-a(p)(R-n), which was asked by Cleanthous et al. in [J. Geom. Anal. 27 (2017), pp. 2758-27871. More precisely, applying the known atomic and finite atomic characterizations of H-a(p)(R-n), the authors prove that the dual space of H-a(p)(R-n), with p is an element of (0, 1](n), is the anisotropic mixed-norm Campanato space L-p,r,s(a) (R-n) for every r is an element of [1, infinity) and s is an element of [nu/alpha(1/p- -1)], infinity) boolean AND z+, where v := a1 + ... +a(n), a- := min{a(1),...,a(n)}, p- := min{p1,..., p(n)} and, for any t is an element of R, [t] denotes the largest integer not greater than t. This duality result is new even for the isotropic mixed-norm Hardy spaces on R-n.