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

@article{d1f236cf34a243de9328ba12828ccbee,

title = "A study of Jacobians in Hardy-Orlicz spaces",

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.",

author = "Tadeusz Iwaniec and Anna Verde",

year = "1999",

month = dec,

day = "1",

language = "English (US)",

volume = "129",

pages = "539--570",

journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",

issn = "0308-2105",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

T1 - A study of Jacobians in Hardy-Orlicz spaces

AU - Iwaniec, Tadeusz

AU - Verde, Anna

PY - 1999/12/1

Y1 - 1999/12/1

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.

UR - http://www.scopus.com/inward/record.url?scp=22644450595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22644450595&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22644450595

SN - 0308-2105

VL - 129

SP - 539

EP - 570

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 3

ER -

A study of Jacobians in Hardy-Orlicz spaces

Abstract

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this