Mellin pseudodifferential operators techniques in the theory of singular integral operators on some Carleson curves. (English) Zbl 0906.47037
Gohberg, I. (ed.) et al., Differential and integral operators. Vol. I. Proceedings of the international workshop on operator theory and applications, IWOTA 95, Regensburg, Germany, July 31-August 4, 1995. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 102, 201-218 (1998).
Summary: We consider an algebra \({\mathcal A}_p(\Gamma,\omega)\) of singular integral operators with slowly oscillating bounded coefficients acting in \(L_p(\Gamma,\omega)\), \(1< p<\infty\), where \(\Gamma\) is a composed Carleson curve with logarithmic whirl points and \(\omega\) is a power weight. The local analysis of operators \(A\in{\mathcal A}_p(\Gamma,\omega)\) at singular points of the contours is based on the Mellin pseudodifferential operators method. This method gives effective formulas for the local symbols. These formulas describe the influence on the local symbol of both the curve and the weight in an explicit form.
For the entire collection see [Zbl 0883.00019].
For the entire collection see [Zbl 0883.00019].
MSC:
| 47G30 | Pseudodifferential operators |
| 47A56 | Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) |
