Hardy factorization in terms of fractional commutators in Lorentz spaces

Abstract

We provide a constructive proof of H^1\left({\text{ℝ}}^d\right) (the classical Hardy space) factorization in terms of fractional commutators in Lorentz spaces. As a direct application, we obtain a characterization of functions in BMO space. Furthermore, we also obtain a Lorentz compactness characterization of fractional commutators.

Keywords

BMO / CMO / Lorentz space / commutator / Hardy space / Riesz potential

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Higher Education Press