Abstract
We obtain a new square function characterization of the weak Hardy space \(H^{p,\infty }\) for all \(p\in (0,\infty )\). This space consists of all tempered distributions whose smooth maximal function lies in weak \(L^p\). Our proof is based on interpolation between \(H^p\) spaces. The main difficulty we overcome is the lack of a good dense subspace of \(H^{p,\infty }\) which forces us to work with general \(H^{p,\infty }\) distributions.
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Acknowledgments
I want to express my deepest gratitude to Professor L. Grafakos, who gave me a lot of valuable suggestions. Without him I could not have finished this article.
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Communicated by Rodolfo H. Torres.
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He, D. Square Function Characterization of Weak Hardy Spaces. J Fourier Anal Appl 20, 1083–1110 (2014). https://doi.org/10.1007/s00041-014-9346-1
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DOI: https://doi.org/10.1007/s00041-014-9346-1