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

Astala, 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 &lt; p &lt; ∞) if and only if Γ is regular, i.e.,H1(Γ ∩ B(z0,R) ≤ CRfor every z0 ∈ C, R &gt; 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 &lt; p &lt; ∞) if and only if Γ is regular, i.e.,H1(Γ ∩ B(z0,R) ≤ CRfor every z0 ∈ C, R &gt; 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 -