caa a22 4500 467932204 CHVBK 20180406152946.0 cr unu---uuuuu 170328e20060401xx s 000 0 eng 10.1007/s00020-004-1361-1 doi (NATIONALLICENCE)springer-10.1007/s00020-004-1361-1 Luther U. Fakultät für Mathematik, Technische Universität Chemnitz, D-09107, Chemnitz, Germany aut Weakly Singular Integral Operators in Weighted L∞-Spaces [Elektronische Daten] [U. Luther] Abstract.: We study integral operators on (−1, 1) with kernels k(x, t) which may have weak singularities in (x, t) with x ∈N1, t ∈N2, or x=t, where N1,N2 are sets of measure zero. It is shown that such operators map weighted L∞-spaces into certain weighted spaces of smooth functions, where the degree of smoothness is the higher the smoother the kernel k(x, t) as a function in x is. 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. Birkhäuser Verlag, Basel, 2006 Weakly singular integral operators nationallicence weighted spaces of continuous functions nationallicence approximation spaces nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 541-554 0378-620X 54:4<541 2006 54 20 https://doi.org/10.1007/s00020-004-1361-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-004-1361-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Luther U. Fakultät für Mathematik, Technische Universität Chemnitz, D-09107, Chemnitz, Germany aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; www.birkhauser.ch 54/4(2006-04-01), 541-554 0378-620X 54:4<541 2006 54 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer