Variable anisotropic Herz-Morrey-Hardy spaces and their applications (Q6569648)

In the paper, the author introduces the homogeneous and non-homogeneous version of the variable anisotropic Herz-Morrey-Hardy spaces, \(HM\dot{K}^{\alpha(\cdot)q}_{p(\cdot),\lambda}(A,\mathbb{R}^n)\) and \(HMK^{\alpha(\cdot)q}_{p(\cdot),\lambda}(A,\mathbb{R}^n)\), respectively. Here, \(A\) denotes an expansive dilation operator on \(\mathbb{R}^n\), \(\alpha(\cdot) \in L^{\infty}(\mathbb{R}^n)\), \(p(\cdot): \mathbb{R}^n \longrightarrow (0,+\infty)\) is a variable exponent function satisfying the globally log-Hölder continuous condition, and \(q,\ \lambda \in (0,\infty]\).\N\NThe spaces are introduced by means of the non-tangential grand maximal function belonging to Herz-Morrey variable spaces introduced in [\textit{H. Wang}, Commun. Math. Anal. 18, No. 2, 1--14 (2015; Zbl 1344.46026)]. The atomic decompositions of these Hardy-type spaces are proved and, as an application, the boundedness of some sublinear operators defined on them is shown.