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arXiv · 0910.5313

Equivalence of norms on finite linear combinations of atoms

G. Mauceri·S. Meda
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Abstract

Let M be a space of homogeneous type and denote by F^\infty_{cont}(M) the space of finite linear combinations of continuous (1,\infty)-atoms. In this note we give a simple function theoretic proof of the equivalence on F^\infty_{cont}(M) of the H^1-norm and the norm defined in terms of finite linear combinations of atoms. The result holds also for the class of nondoubling metric measure spaces considered in previous works of A. Carbonaro and the authors.

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G. Mauceri, S. Meda. 2010-04-03. Equivalence of norms on finite linear combinations of atoms. https://arxiv.org/abs/0910.5313

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