Atomic decomposition of vector Hardy spaces
نویسندگان
چکیده
منابع مشابه
A New Proof of the Atomic Decomposition of Hardy Spaces
A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.
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An atomic decomposition is considered in Banach space. A method for constructing an atomic decomposition of Banach space, starting with atomic decomposition of subspaces is presented. Some relations between them are established. The proposed method is used in the study of the frame properties of systems of eigenfunctions and associated functions of discontinuous differential operators.
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Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized an...
متن کاملM ATHEMATICS I NSTITUTE 2014 : 04 A New Proof of the Atomic Decomposition of Hardy Spaces
A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.
متن کاملAtomic Decomposition and Boundedness Criterion of Operators on Multi-parameter Hardy Spaces of Homogeneous Type
The main purpose of this paper is to derive a new (p, q)-atomic decomposition on the multi-parameter Hardy space H(X1 ×X2) for 0 < p0 < p ≤ 1 for some p0 and all 1 < q < ∞, where X1 × X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L(X1 × X2) (for 1 < q < ∞) and Hardy space H(X1 × X2) (for 0 < p ≤ 1). As an application,...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.02.017