# 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

, Volume 16 (2) – Mar 16, 2011
32 pages

/lp/springer_journal/duality-of-weighted-anisotropic-besov-and-triebel-lizorkin-spaces-J4o0CFweQx
Publisher
SP Birkhäuser Verlag Basel
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Fourier Analysis; Operator Theory; Econometrics; Potential Theory
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-011-0119-7
Publisher site
See Article on Publisher Site

### Abstract

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 $${{\mathbb R}^n}$$ .

### Journal

PositivitySpringer Journals

Published: Mar 16, 2011

### References

• Wavelet frames for distributions in anisotropic Besov spaces
Haroske, D.D.; Tamási, E.

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations