Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves

Tao Qian

Studia Mathematica (1997)

  • Volume: 123, Issue: 3, page 195-216
  • ISSN: 0039-3223

Abstract

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The paper presents a theory of Fourier transforms of bounded holomorphic functions defined in sectors. The theory is then used to study singular integral operators on star-shaped Lipschitz curves, which extends the result of Coifman-McIntosh-Meyer on the -boundedness of the Cauchy integral operator on Lipschitz curves. The operator theory has a counterpart in Fourier multiplier theory, as well as a counterpart in functional calculus of the differential operator 1/i d/dz on the curves.

How to cite

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Qian, Tao. "Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves." Studia Mathematica 123.3 (1997): 195-216. <http://eudml.org/doc/216389>.

@article{Qian1997,
abstract = {The paper presents a theory of Fourier transforms of bounded holomorphic functions defined in sectors. The theory is then used to study singular integral operators on star-shaped Lipschitz curves, which extends the result of Coifman-McIntosh-Meyer on the $L^2$-boundedness of the Cauchy integral operator on Lipschitz curves. The operator theory has a counterpart in Fourier multiplier theory, as well as a counterpart in functional calculus of the differential operator 1/i d/dz on the curves.},
author = {Qian, Tao},
journal = {Studia Mathematica},
keywords = {singular integrals; Fourier multipliers; Cauchy integral operator; Lipschitz curves},
language = {eng},
number = {3},
pages = {195-216},
title = {Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves},
url = {http://eudml.org/doc/216389},
volume = {123},
year = {1997},
}

TY - JOUR
AU - Qian, Tao
TI - Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves
JO - Studia Mathematica
PY - 1997
VL - 123
IS - 3
SP - 195
EP - 216
AB - The paper presents a theory of Fourier transforms of bounded holomorphic functions defined in sectors. The theory is then used to study singular integral operators on star-shaped Lipschitz curves, which extends the result of Coifman-McIntosh-Meyer on the $L^2$-boundedness of the Cauchy integral operator on Lipschitz curves. The operator theory has a counterpart in Fourier multiplier theory, as well as a counterpart in functional calculus of the differential operator 1/i d/dz on the curves.
LA - eng
KW - singular integrals; Fourier multipliers; Cauchy integral operator; Lipschitz curves
UR - http://eudml.org/doc/216389
ER -

References

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  3. [CMcM] R. Coifman, A. McIntosh et Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361-387. 
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