The dualities between variable anisotropic Hardy and Campanato spaces with variable exponents

Let $$\Theta $$ Θ be a continuous multi-level ellipsoid cover of $$\mathbb {R}^n$$ R n , $$p(\cdot ):\mathbb {R}^{n}\rightarrow (0,\,\infty ]$$ p ( · ) : R n → ( 0 , ∞ ] be a variable exponent function satisfying the globally $$\log $$ log -Hölder continuous condition, and let $$\mathcal {H}^{p(\cdot )}(\Theta )$$ H p ( · ) ( Θ ) be the variable anisotropic Hardy space with variable exponent introduced by Yang et al. (Anal Geom Metr Spaces 9:65–89, 2021). In this article, the authors obtain the dual spaces of $$\mathcal {H}^{p(\cdot )}(\Theta )$$ H p ( · ) ( Θ ) . In addition, the authors also establish a boundedness criterion of a class of linear operators from $$\mathcal {H}^{p(\cdot )}(\Theta )$$ H p ( · ) ( Θ ) to $$L^{p(\cdot )}({{\mathbb {R}}^n})$$ L p ( · ) ( R n ) .