The cauchy transform on bounded domains

J. M. Anderson; A. Hinkkanen

doi:10.1090/S0002-9939-1989-0972226-5

The cauchy transform on bounded domains

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

Abstract

Suppose that ƒ is in L²(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ₂ ≤ (2/α)ƖƖƒƖƖ₂, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.

Original language	English (US)
Pages (from-to)	179-185
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	107
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1989-0972226-5
State	Published - Sep 1989
Externally published	Yes

Keywords

Link homotopy
Links
Whitney trick

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Online availability

10.1090/S0002-9939-1989-0972226-5

Library availability

Discover UIUC Full Text

Cite this

@article{cab9815643c0455aa2a6afacc741daa2,

title = "The cauchy transform on bounded domains",

abstract = "Suppose that ƒ is in L2(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ2 ≤ (2/α)ƖƖƒƖƖ2, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.",

keywords = "Link homotopy, Links, Whitney trick",

author = "Anderson, {J. M.} and A. Hinkkanen",

year = "1989",

month = sep,

doi = "10.1090/S0002-9939-1989-0972226-5",

language = "English (US)",

volume = "107",

pages = "179--185",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - The cauchy transform on bounded domains

AU - Anderson, J. M.

AU - Hinkkanen, A.

PY - 1989/9

Y1 - 1989/9

N2 - Suppose that ƒ is in L2(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ2 ≤ (2/α)ƖƖƒƖƖ2, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.

AB - Suppose that ƒ is in L2(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ2 ≤ (2/α)ƖƖƒƖƖ2, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.

KW - Link homotopy

KW - Links

KW - Whitney trick

UR - http://www.scopus.com/inward/record.url?scp=84966230068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966230068&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1989-0972226-5

DO - 10.1090/S0002-9939-1989-0972226-5

M3 - Article

AN - SCOPUS:84966230068

SN - 0002-9939

VL - 107

SP - 179

EP - 185

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

The cauchy transform on bounded domains

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this