Atomic, molecular and wavelet decomposition of generalized 2-microlocal Besov spaces
نویسندگان
چکیده
منابع مشابه
Entropy numbers of embeddings of some 2-microlocal Besov spaces
We investigate compactness and asymptotic behaviour of the entropy numbers of embeddings B s1,s1 p1,q1 (R, U) ↪→ B s2,s2 p2,q2 (R, U) . Here B ′ p,q (Rn, U) denotes a 2-microlocal Besov space with a weight given by the distance to a fixed set U ⊂ Rn.
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We give a corrected proof of Lemma 3.1 in [1]. While the statement of [1, Lemma 3.1] is true, its proof is incorrect. The argument contains a serious defect which can not be easily corrected. The inequality that appears in [1] before (3.5) is not true. If this inequality was true, then we could conclude that, even for a non doubling measure μ, (3.5) was also true. But there exist some non doubl...
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In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spac...
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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2010
ISSN: 0972-6802
DOI: 10.1155/2010/469513