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

Loading next page...
 
/lp/springer_journal/duality-of-weighted-anisotropic-besov-and-triebel-lizorkin-spaces-J4o0CFweQx
Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Basel AG
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
discover and read the research
that matters to you.

Enjoy affordable access to
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.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off