In this article, the authors introduce the Orlicz Calderón-Hardy spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msubsup> <mrow> <mrow> <mi mathvariant="script">H</mi> </mrow> </mrow> <mrow> <mi>q</mi> <mo>,</mo> <mn>2</mn> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">Φ</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> and investigate their properties. As an application, for m ∈ ℕ, the authors show that the iterated Laplacian Δm is bijective from Orlicz Calderón-Hardy spaces <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msubsup> <mrow> <mrow> <mi mathvariant="script">H</mi> </mrow> </mrow> <mrow> <mi>q</mi> <mo>,</mo> <mn>2</mn> <mi>m</mi> </mrow> <mrow> <mi mathvariant="normal">Φ</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> to corresponding Orlicz-Hardy spaces HΦ(ℝn).

Orlicz Calderón-Hardy Spaces

期刊论文
发表日期：

2025年7月15日

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Zirong Liu,
Ziyi He,
Huixia Mo

摘要

In this article, the authors introduce the Orlicz Calderón-Hardy spaces ${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$ $H_{q, 2 m}^{Φ} (R^{n})$ 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 ${\cal{H}}_{q,2m}^{\Phi}(\mathbb{R}^{n})$ $H_{q, 2 m}^{Φ} (R^{n})$ to corresponding Orlicz-Hardy spaces H^Φ(ℝⁿ).