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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
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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.

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Article copyright: © Copyright 1993 American Mathematical Society

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