A study of Jacobians in Hardy-Orlicz spaces

Tadeusz Iwaniec; Anna Verde

A study of Jacobians in Hardy-Orlicz spaces

Tadeusz Iwaniec, Anna Verde

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

We study the Jacobian determinants J = det(∂fⁱ/∂x_j) of mappings f : Ω ⊂ ℝⁿ → ℝⁿ in a Sobolev-Orlicz space W^1,Φ(Ω, ℝⁿ). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy-Orlicz spaces H^P(Ω). Other nonlinear quantities involving the Jacobian, such as J log|J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.

Original language	English (US)
Pages (from-to)	539-570
Number of pages	32
Journal	Royal Society of Edinburgh - Proceedings A
Volume	129
Issue number	3
State	Published - Dec 1 1999

ASJC Scopus subject areas

Mathematics(all)

Cite this

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abstract = "We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f : Ω ⊂ ℝn → ℝn in a Sobolev-Orlicz space W1,Φ(Ω, ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy-Orlicz spaces HP(Ω). Other nonlinear quantities involving the Jacobian, such as J log|J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.",

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N2 - We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f : Ω ⊂ ℝn → ℝn in a Sobolev-Orlicz space W1,Φ(Ω, ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy-Orlicz spaces HP(Ω). Other nonlinear quantities involving the Jacobian, such as J log|J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.

AB - We study the Jacobian determinants J = det(∂fi/∂xj) of mappings f : Ω ⊂ ℝn → ℝn in a Sobolev-Orlicz space W1,Φ(Ω, ℝn). Their natural generalizations are the wedge products of differential forms. These products turn out to be in the Hardy-Orlicz spaces HP(Ω). Other nonlinear quantities involving the Jacobian, such as J log|J|, are also studied. In general, the Jacobians may change sign and in this sense our results generalize the existing ones concerning positive Jacobians.

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A study of Jacobians in Hardy-Orlicz spaces

Abstract

ASJC Scopus subject areas

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