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arXiv · 1502.07542

A Note on Hardy Spaces and Bounded Operators

Pablo Rocha
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Abstract

In this note we show that if f belongs to Hp(Rn)\capLs(Rn), where 0 < p <= 1 < s < 1, then there exists a (p;infinite)-atomic decomposition which converges to f in Ls(Rn). From this fact, we prove that a bounded operator T on Ls(Rn) can be extended to a bounded operator from Hp(Rn) into Lp(Rn) if and only if T is bounded uniformly in Lp norm on all (p;infinite)-atoms. A similar result is also obtained from Hp(Rn) into Hp(Rn).

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Pablo Rocha. 2015-02-26. A Note on Hardy Spaces and Bounded Operators. https://arxiv.org/abs/1502.07542

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