The Hardy space H1 on non-homogeneous metric spaces

By Tuomas Hytönen, Dachun Yang, Dongyong Yang. Mathematical Proceedings of the Cambridge Philosophical Society, 2010

99 citations recorded by the source corpus.

Abstract Let (, d, μ) be a metric measure space and satisfy the so-called upper doubling condition and the geometrical doubling condition. We introduce the atomic Hardy space H1(μ) and prove that its dual space is the known space RBMO(μ) in this context. Using this duality, we establish a criterion for the boundedness of linear operators from H1(μ) to any Banach space. As an application of this criterion, we obtain the boundedness of Calderón–Zygmund operators from H1(μ) to L1(μ).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d9b3f29f149ba5a5bd7698d4525c03cc39586af8

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In Applied Mathematics

1. Wen Yuan
2. Dachun Yang
3. Xing Fu
4. Yoshihiro Sawano
5. Jun Liu
6. Ciqiang Zhuo
7. Yangyang Zhang
8. Yuan Zhou

In Mathematical Physics

1. Wen Yuan
2. Dachun Yang
3. Xing Fu
4. Yoshihiro Sawano
5. Ciqiang Zhuo
6. Jun Liu
7. Yangyang Zhang
8. Songbai Wang

Citations in the corpus

• GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “lso an upper doubling space by taking the dominating function λ(x,r) := C0rκ. (ii) Let (X,d,µ) be upper doubling with λ being the dominating function on X ×(0,∞) as in Definition 1.3. It was proved in [21] that there exists another dominating function eλ such that eλ≤ λ, C λe ≤ Cλ and, for all x, y ∈”