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

Volume 123 / 1997

Tao Qian Studia Mathematica 123 (1997), 195-216 DOI: 10.4064/sm-123-3-195-216


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.


  • Tao Qian

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