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arXiv · 0801.1745

On the H^1-L^1 boundedness of operators

S. Meda·P. Sjogren·M. Vallarino
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Abstract

We prove that if q is in (1,\infty), Y is a Banach space and T is a linear operator defined on the space of finite linear combinations of (1,q)-atoms in R^n which is uniformly bounded on (1,q)-atoms, then T admits a unique continuous extension to a bounded linear operator from H^1(R^n) to Y. We show that the same is true if we replace (1,q)-atoms with continuous (1,\infty)-atoms. This is known to be false for (1,\infty)-atoms.

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S. Meda, P. Sjogren, M. Vallarino. 2008-01-11. On the H^1-L^1 boundedness of operators. https://arxiv.org/abs/0801.1745

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