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

Qian, Tao

Studia Mathematica, Tome 122 (1997), p. 195-216 / Harvested from The Polish Digital Mathematics Library

Résumé

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.

Détail

Publié le : 1997-01-01

Zbl 0924.42012

EUDML-ID : urn:eudml:doc:216389

Bibliographie

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