Atomic decomposition of vector Hardy spaces

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• 作者：Salvador Pé ; rez-Esteva ^{salvador@matcuer.unam.mx} ; Hugo Ocampo-Salgado ; ^{ocampo@matcuer.unam.mx} ; ^{hugoocampo10@gmail.com}
• 关键词：Vector Hardy spaces ; Atomic decompositions
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：15 July, 2013
• 年：2013
• 卷：403
• 期：2
• 页码：408-422
• 全文大小：451 K

文摘

We study Banach-valued Hardy spaces of harmonic functions in the upper half space of defined in terms of maximal functions and the corresponding space of distributional boundary limits , where is an arbitrary real or complex Banach space. For the elements of are the Poisson transform of Borel measures with -bounded variation and values in . For we prove the existence of atomic decomposition of elements in where the atoms are vector measures with certain size and cancellation properties that generalize the atoms in the real valued Hardy spaces.