Duality of weighted anisotropic Besov and Triebel–Lizorkin spaces

Duality of weighted anisotropic Besov and Triebel–Lizorkin spaces Let A be an expansive dilation on $${{\mathbb R}^n}$$ and w a Muckenhoupt $${\mathcal A_\infty(A)}$$ weight. In this paper, for all parameters $${\alpha\in{\mathbb R} }$$ and $${p,q\in(0,\infty)}$$ , the authors identify the dual spaces of weighted anisotropic Besov spaces $${\dot B^\alpha_{p,q}(A;w)}$$ and Triebel–Lizorkin spaces $${\dot F^\alpha_{p,q}(A;w)}$$ with some new weighted Besov-type and Triebel–Lizorkin-type spaces. The corresponding results on anisotropic Besov spaces $${\dot B^\alpha_{p,q}(A; \mu)}$$ and Triebel–Lizorkin spaces $${\dot F^\alpha_{p,q}(A; \mu)}$$ associated with $${\rho_A}$$ -doubling measure μ are also established. All results are new even for the classical weighted Besov and Triebel–Lizorkin spaces in the isotropic setting. In particular, the authors also obtain the $${\varphi}$$ -transform characterization of the dual spaces of the classical weighted Hardy spaces on $${{\mathbb R}^n}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Duality of weighted anisotropic Besov and Triebel–Lizorkin spaces

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SP Birkhäuser Verlag Basel
Copyright © 2011 by Springer Basel AG
Mathematics; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Operator Theory; Econometrics; Potential Theory
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  • Wavelet frames for distributions in anisotropic Besov spaces
    Haroske, D.D.; Tamási, E.

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