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

Studia Mathematica (1997)

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

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topQian, 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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- [CM2] R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentiels, Astérisque 57 (1978). Zbl0483.35082
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