Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves
Studia Mathematica, Tome 123 (1997) no. 3, pp. 195-216
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
@article{10_4064_sm_123_3_195_216,
author = {Tao Qian},
title = {Singular integrals with holomorphic kernels and {Fourier} multipliers on star-shaped closed {Lipschitz} curves},
journal = {Studia Mathematica},
pages = {195--216},
year = {1997},
volume = {123},
number = {3},
doi = {10.4064/sm-123-3-195-216},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-123-3-195-216/}
}
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Tao Qian. Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves. Studia Mathematica, Tome 123 (1997) no. 3, pp. 195-216. doi: 10.4064/sm-123-3-195-216
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