- Tytuł:
- Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves
- Autorzy:
-
Gaudry, Garth
Qian, Tao
Wang, Silei - Powiązania:
- https://bibliotekanauki.pl/articles/966841.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- The aim of this paper is to study singular integrals T generated by holomorphic kernels defined on a natural neighbourhood of the set ${zζ^{-1}: z, ζ ∈ , z ≠ ζ}$, where is a star-shaped Lipschitz curve, $ ={ 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) $TF(z)= p.v. ∫_ (zη^{-1})F(η)(dη/η).$ We identify a class of kernels of the stated type that give rise to bounded operators on $L^{2} (,|d|)$. We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.
- Źródło:
-
Colloquium Mathematicum; 1996, 70, 1; 133-150
0010-1354 - Pojawia się w:
- Colloquium Mathematicum
- Dostawca treści:
- Biblioteka Nauki
Artykuł