Atomic decomposition of vector Hardy spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Perez-Esteva, Salvador¹  Ocarnpo-Salgado, Hugo¹ 

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Cuernavaca 62251, Mexico

关键词: Vector Hardy spaces;    Atomic decompositions;   

DOI  :  10.1016/j.jmaa.2013.02.017

来源: Elsevier

【 摘 要 】

We study Banach-valued Hardy spaces h(X)(p)(R-+(n+1)) of harmonic functions in the upper half space of Rn+1 defined in terms of maximal functions and the corresponding space of distributional boundary limits H-X(p)(R-n), where X is an arbitrary real or complex Banach space. For p > 1 the elements of h(X)(p)(R-+(n+1)) are the Poisson transform of Borel measures with p-bounded variation and values in X. For p <= 1 we prove the existence of atomic decomposition of elements in H-X(p)(R-n) where the atoms are vector measures with certain size and cancellation properties that generalize the atoms in the real valued Hardy spaces. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free