Equivalence of norms on finite linear combinations of atoms

Details Equivalence of norms on finite linear combinations of atoms Equivalence of norms on finite linear combinations of atoms

2009-10-28

arxiv.org/abs/0910.5313v2

Mathematics

Functional Analysis

10 pages, revised argument

Scientific paper

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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