Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Besov spaces on domains in $ {\bf R}\sp d$


Authors: Ronald A. DeVore and Robert C. Sharpley
Journal: Trans. Amer. Math. Soc. 335 (1993), 843-864
MSC: Primary 46E35
MathSciNet review: 1152321
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study Besov spaces $ B_q^\alpha ({L_p}(\Omega ))$, $ 0 < p,q,\alpha < \infty $, on domains $ \Omega $ in $ {\mathbb{R}^d}$ . We show that there is an extension operator $ \mathcal{E}$ which is a bounded mapping from $ B_q^\alpha ({L_p}(\Omega ))$ onto $ B_q^\alpha ({L_p}({\mathbb{R}^d}))$. This is then used to derive various properties of the Besov spaces such as interpolation theorems for a pair of $ B_q^\alpha ({L_p}(\Omega ))$, atomic decompositions for the elements of $ B_q^\alpha ({L_p}(\Omega ))$, and a description of the Besov spaces by means of spline approximation.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E35

Retrieve articles in all journals with MSC: 46E35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1152321-6
Article copyright: © Copyright 1993 American Mathematical Society