Luther, Uwe : Weakly Singular Integral Operators in Weighted $L^\infty$--Spaces
- Author(s):
-
Luther, Uwe
- Title:
- Weakly Singular Integral Operators in Weighted $L^\infty$--Spaces
- Electronic source:
-
application/postscript
application/pdf
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 12, 2003
- Mathematics Subject Classification:
-
45A05 [ Linear integral equations ] 45E99 [ None of the above, but in this section ] - Abstract:
- We study integral operators on $(-1,1)$ with kernels $k(x,t)$ which may have weak singularities in $(x,t)$ with $x\in N_1$, $t\in N_2$, or $x=t$, where $N_1,N_2$ are sets of measure zero. It is shown that such operators map weighted $\fL^\infty$--spaces into certain weighted spaces of smooth functions, where the degree of smoothness is as higher as smoother the kernel $k(x,t)$ as a function in $x$. The spaces of smooth function are generalizations of the Ditzian-Totik spaces which are defined in terms of the errors of best weighted uniform approximation by algebraic polynomials.
- Keywords:
- Weakly singular integral operators,
Weighted spaces of continuous functions, Approximation spaces
- Language:
-
English
- Publication time:
- 12 / 2003
