Orlicz Calderón-Hardy Spaces

Abstract

In this article, the authors introduce the Orlicz Calderón-Hardy spaces ${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$ and investigate their properties. As an application, for m ∈ ℕ, the authors show that the iterated Laplacian Δ^m is bijective from Orlicz Calderón-Hardy spaces ${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$ to corresponding Orlicz-Hardy spaces H^Φ(ℝⁿ).

Keywords

Calderón-Hardy space / Young function / iterated Laplacian / Orlicz-Hardy space / fundamental solution / 42B25 / 42B30 / 42B37

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Peking University