Duality of weighted anisotropic Besov and Triebel-Lizorkin spaces. (English) Zbl 1260.46025
Let \(A\) be an expansive anisotropic dilation matrix in \(\mathbb R^n\) (the absolute values of all eigenvalues are larger than 1) and \(w\in {\mathcal A}_\infty (A)\) an anisotropic Muckenhoupt weight adapted to \(A\). Let \(\dot{B}^\alpha_{p,q} (A; w)\) and \(\dot{F}^\alpha_{p,q} (A; w)\) with \(\alpha \in \mathbb R\) and \(0<p,q< \infty\) be the related homogeneous anisotropic weighted spaces. Let \(\dot{B}^{\alpha, \tau}_{p,q} (A; w)\) and \(\dot{F}^{\alpha, \tau}_{p,q} (A; w)\) with \(\tau \geq 0\) be the corresponding morreyfied spaces. It is the main aim of this paper to identify the dual spaces \(\dot{B}^\alpha_{p,q} (A;w)^*\) and \(\dot{F}^\alpha_{p,q} (A; w)^*\) with some of these morreyfied spaces, (Theorems 2.1 and 2.2). There are corresponding assertions with doubling measures \(\mu\) in place of the weight \(w\).
Reviewer: Hans Triebel (Jena)
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 42B35 | Function spaces arising in harmonic analysis |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 46E39 | Sobolev (and similar kinds of) spaces of functions of discrete variables |
Keywords:
anisotropic weighted Besov spaces; anisotropic weighted Triebel-Lizorkin spaces; Muckenhoupt weights; dual spacesReferences:
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