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Singular integrals on the complex affine group

100%

Gaudry G., Sjögren P.

Colloquium Mathematicum

1998

tom 75

nr 1

133-148

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

81%

Gaudry G., Qian T., Wang S.

Colloquium Mathematicum

1996

tom 70

nr 1

133-150

The aim of this paper is to study singular integrals T generated by holomorphic kernels 𝛷 defined on a natural neighbourhood of the set ${zζ^{-1}: z, ζ ∈ 𝛤, z ≠ ζ}$, where 𝛤 is a star-shaped Lipschitz curve, $𝛤 ={ exp(iz) : z = x+iA(x), A' ∈ L^{∞}[-π,π], A(-π ) =A(π)}$. Under suitable conditions on F and z, the operators are given by (1) $TF(z)= p.v. ∫_𝛤 𝛷(zη^{-1})F(η)(dη/η).$ We identify a class of kernels of the stated type that give rise to bounded operators on $L^{2} (𝛤,|d𝛤|)$. We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Gaudry G.

1 Qian T.

1 Sjögren P.

1 Wang S.

1 1998

1 1996

Wyniki wyszukiwania

Singular integrals on the complex affine group

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