Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves

Gaudry, Garth; Qian, Tao; Wang, Silei

Colloquium Mathematicae, Tome 70 (1996), p. 133-150 / Harvested from The Polish Digital Mathematics Library

Résumé

The aim of this paper is to study singular integrals T generated by holomorphic kernels defined on a natural neighbourhood of the set $z ζ^{- 1} : z, ζ \in, z \neq ζ$ , where is a star-shaped Lipschitz curve, $= e x p (i z) : z = x + i A (x), A^{'} \in L^{\infty} [- π, π], A (- π) = A (π)$ . Under suitable conditions on F and z, the operators are given by (1) $T F (z) = p . v . \int_{(} z η^{- 1}) F (η) (d η / η) .$ We identify a class of kernels of the stated type that give rise to bounded operators on $L^{2} (, | d |)$ . We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.

Publié le : 1996-01-01

Zbl 0860.42013

EUDML-ID : urn:eudml:doc:210391

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     author = {Garth Gaudry and Tao Qian and Silei Wang},
     title = {Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves},
     journal = {Colloquium Mathematicae},
     volume = {70},
     year = {1996},
     pages = {133-150},
     zbl = {0860.42013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv70i1p133bwm}
}

Gaudry, Garth; Qian, Tao; Wang, Silei. Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves. Colloquium Mathematicae, Tome 70 (1996) pp. 133-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv70i1p133bwm/

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