Summary
We define as a distribution the product of a function (or distribution) h in some Hardy space \(\mathcal{H}^p\) with a function b in the dual space of \(\mathcal{H}^p\). Moreover, we prove that the product b × h may be written as the sum of an integrable function with a distribution that belongs to some Hardy–Orlicz space, or to the same Hardy space \(\mathcal{H}^p\), depending on the values of p.
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Bonami, A., Feuto, J. (2010). Products of Functions in Hardy and Lipschitz or BMO Spaces. In: Cabrelli, C., Torrea, J. (eds) Recent Developments in Real and Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4588-5_4
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DOI: https://doi.org/10.1007/978-0-8176-4588-5_4
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