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Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2005)

Abstract

Similarly to [164, Sects. 4, 5] and [165, Sects. 5, 6], in this section, we introduce the inhomogeneous Besov-Hausdorff space \(BH_{p, q}^{s, \tau }({\mathbb{R}}^ n)\) and the Triebel-Lizorkin-Hausdorff space \(FH_{p,q}^{s,\tau } (\mathbb{R}^n )\), whose dual spaces are, respectively, certain Besov-type space and Triebel-Lizorkin-type space when \(p \,\, \in \,\, (1, \,\, \infty), \,\, q \,\, \in \,\, \left[ \left.1, \,\, \infty \right. \right) \,\, s \,\, \in \,\, \mathbb{R}\) and \(\tau \in \left[ {0,\frac{1} {{(p \vee q)\prime}}} \right]\). Recall that \((p \vee q)^\prime\) denotes the conjugate index of \(p \vee q\), namely, \(\frac{1}{p \vee q} + \frac{1}{p \vee q^\prime} = 1\). The spaces \(BH_{p, q}^{s, \tau }({\mathbb{R}}^n)\) and \(FH_{p, q}^{s, \tau }({\mathbb{R}}^n)\) have some properties similar to those of \(A_{p, q}^{s, \tau }({\mathbb{R}}^ n)\), which include the ϕ-transform characterization, embedding properties, smooth atomic and molecular decompositions.

Keywords

  • Besov Space
  • Atomic Decomposition
  • Dyadic Cube
  • Real Interpolation
  • Disjoint Interior

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Dachun Yang .

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© 2011 Springer-Verlag Berlin Heidelberg

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Yuan, W., Sickel, W., Yang, D. (2011). Inhomogeneous Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces. In: Morrey and Campanato Meet Besov, Lizorkin and Triebel. Lecture Notes in Mathematics(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14606-0_7

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