# Calderón's problem for Lipschitz classes and the dimension of quasicircles.

Revista Matemática Iberoamericana (1988)

- Volume: 4, Issue: 3-4, page 469-486
- ISSN: 0213-2230

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topAstala, Kari. "Calderón's problem for Lipschitz classes and the dimension of quasicircles.." Revista Matemática Iberoamericana 4.3-4 (1988): 469-486. <http://eudml.org/doc/39366>.

@article{Astala1988,

abstract = {In the last years the mapping properties of the Cauchy integralCΓf(z) = 1/(2πi) ∫Γ [f(ξ) / ξ - z] dξhave been widely studied. The most important question in this area was Calderón's problem, to determine those rectifiable Jordan curves Γ for which CΓ defines a bounded operator on L2(Γ). The question was solved by Guy David [Da] who proved that CΓ is bounded on L2(Γ) (or on Lp(Γ), 1 < p < ∞) if and only if Γ is regular, i.e.,H1(Γ ∩ B(z0,R) ≤ CRfor every z0 ∈ C, R > 0 and for some constant C (...).},

author = {Astala, Kari},

journal = {Revista Matemática Iberoamericana},

keywords = {Integrales singulares; Integral de Cauchy; Dominios de Lipschitz; quasicircle},

language = {eng},

number = {3-4},

pages = {469-486},

title = {Calderón's problem for Lipschitz classes and the dimension of quasicircles.},

url = {http://eudml.org/doc/39366},

volume = {4},

year = {1988},

}

TY - JOUR

AU - Astala, Kari

TI - Calderón's problem for Lipschitz classes and the dimension of quasicircles.

JO - Revista Matemática Iberoamericana

PY - 1988

VL - 4

IS - 3-4

SP - 469

EP - 486

AB - In the last years the mapping properties of the Cauchy integralCΓf(z) = 1/(2πi) ∫Γ [f(ξ) / ξ - z] dξhave been widely studied. The most important question in this area was Calderón's problem, to determine those rectifiable Jordan curves Γ for which CΓ defines a bounded operator on L2(Γ). The question was solved by Guy David [Da] who proved that CΓ is bounded on L2(Γ) (or on Lp(Γ), 1 < p < ∞) if and only if Γ is regular, i.e.,H1(Γ ∩ B(z0,R) ≤ CRfor every z0 ∈ C, R > 0 and for some constant C (...).

LA - eng

KW - Integrales singulares; Integral de Cauchy; Dominios de Lipschitz; quasicircle

UR - http://eudml.org/doc/39366

ER -

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