Luther, Uwe : Cauchy Singular Integral Operators in Weighted Spaces of Continuous Functions
- Author(s):
-
Luther, Uwe
- Title:
- Cauchy Singular Integral Operators in Weighted Spaces of Continuous Functions
- Electronic source:
-
application/postscript
application/pdf
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 9, 2002
- Mathematics Subject Classification:
-
44A15 [ Special transforms ] 46E15 [ Banach spaces of continuous, differentiable or analytic functions ] - Abstract:
- We study the Cauchy singular integral operator $SwI$ on $(-1,1)$, where $|w|$ is a generalized Jacobi weight. This operator is considered in pairs of weighted spaces of continuous functions, where the weights $u$ and $v$ are generalized Jacobi weights with nonnegative exponents such that $|w|=u/v$. We introduce a certain polynomial approximation space which is well appropriated to serve as domain of definition of $SwI$. A description of this space in terms of smoothness properties shows that it can be viewed as a limit case of weighted Besov spaces of continuous functions. We use our results to characterize those of the operators $awI+SbwI$ and $\varrho^{-1}(aw\varrho I+bSw\varrho I)$, $\varrho^{-1}\in b^{-1}\Pi$, which act in certain pairs of Ditzian-Totik type Besov spaces.
- Keywords:
- Cauchy singular integral operators,
Weighted spaces of continuous functions,
Approximation spaces
- Language:
-
English
- Publication time:
- 8 / 2002
