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Continuous Embeddings of Besov-Morrey Function Spaces 被引量：4

Continuous Embeddings of Besov-Morrey Function Spaces
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摘要 We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situation Bp1^s1 （R^d ,w）→MB p2^s2 q2^r2（R^d） for a Muekenhoupt A∞ weight w, with wα（x） = ｜x｜^a, 〉 -d, as a typical example. We study embeddings of spaces of Besov-Morrey type, MB p1^s1 q1^r1（R^d）→MB p2^s2 q2^r2（R^d） and obtain necessary and sufficient conditions for this. Moreover, we can also charaeterise the special weighted situation Bp1^s1 （R^d ,w）→MB p2^s2 q2^r2（R^d） for a Muekenhoupt A∞ weight w, with wα（x） = ｜x｜^a, 〉 -d, as a typical example.
作者 Dorothee D. HAROSKE Leszek SKRZYPCZAK
机构地区 Mathematical Institute Faculty of Mathematics and Computer Science
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1307-1328,共22页 数学学报（英文版）
基金 supported by Heisenberg grant Ha 2794/1-2
关键词 Weighted Besov spaces Besov Morrey spaces continuous embeddings Weighted Besov spaces, Besov Morrey spaces, continuous embeddings
分类号 O177 [理学—基础数学]
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  • 1Edmunds, D. E., Triebel, H.: Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, Cambridge, 1996.
  • 2Haroske, D., Triebel, H.: Entropy numbers in weighted function spaces and eigenvalue distribution of some degenerate pseudodifferential operators I. Math. Nachr., 167, 131-156 (1994).
  • 3Kuhn, Th., Leopold, H.-G., Sickel, W., et al.: Entropy numbers of embeddings of weighted Besov spaces. Constr. Approx., 23, 61-77 (2006).
  • 4Kuhn, Th., Leopold, H.-G., Sickel, W., et al.: Entropy numbers of embeddings of weighted Besov spaces II. Proc. Edinburgh Math. Soc. (2), 49, 331 359 (2006).
  • 5Kuhn, Th., Leopold, H.-G., Sickel, W., et al.: Entropy numbers of embeddings of weighted Besov spaces Ⅲ. Weights of logarithmic type. Math. Z., 255, 1 15 (2007).
  • 6Haroske, D. D., Piotrowska, I.: Atomic decompositions of function spaces with Muckenhoupt weights, and some relations to fractal analysis. Math. Nachr., 281, 1476-1494 (2008).
  • 7Haroske, D. D., Skrzypczak, L.: Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, I. Rev. Mat. Complut., 21(1), 135-177 (2008).
  • 8Haroske, D. D., Skrzypczak, L.: Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights, Ⅱ. General weights. Ann. Acad. Sci. Fenn. Math., 36, 111-138 (2011).
  • 9Haroske, D. D., Skrzypczak, L.: Entropy numbers of embeddings of function spaces with Muckenhoupt weights, Ⅲ. Some limiting cases. J. Funct. Spaces Appl., 9(2), 129-178 (2011).
  • 10Haroske, D. D., Skrzypczak, L.: Spectral theory of some degenerate elliptic operators with local singularities. J. Math. Anal. Appl., 371(1), 282-299 (2010).

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Acta Mathematica Sinica,English Series
2012年 第7期

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