Decompositions and Interpolation

Hasi Wulan and Kehe Zhu
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Hasi Wulan: Shantou University, Department of Mathematics
Kehe Zhu: State University of New York, Albany, Department of Mathematics and Statistics

Chapter Chapter 7 in Mobius Invariant QK Spaces, 2017, pp 163-188 from Springer

Abstract: Abstract In this chapter, we consider the problems of decomposition and interpolation for 𝒬 K $$\mathcal{Q}_{K}$$ spaces. We prove an atomic decomposition for 𝒬 K $$\mathcal{Q}_{K}$$ and 𝒬 K , 0 $$\mathcal{Q}_{K,0}$$ , which enables us to write a function as an infinite series of Bergman kernel functions. We prove another decomposition for functions in 𝒬 K $$\mathcal{Q}_{K}$$ and 𝒬 K , 0 $$\mathcal{Q}_{K,0}$$ , which is an extension of the classical Fefferman-Stein decomposition for BMO to the context of 𝒬 K $$\mathcal{Q}_{K}$$ spaces. We will also consider the problem of interpolation for 𝒬 K $$\mathcal{Q}_{K}$$ spaces.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-58287-0_7

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DOI: 10.1007/978-3-319-58287-0_7

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