Timotin, Dan \(C_ p\)-estimates for certain kernels on local fields. (English) Zbl 0645.47016 Stud. Math. 88, No. 1, 43-50 (1988). This paper extends results of the author concerning certain operators defined by a kernel on \(L^ 2(R^ n)\) [Integral Equations Oper. Theory 9, 295-304 (1986; Zbl 0629.47023)] to the case of operators on \(L^ 2(K)\), where K is some local field (i.e. a locally compact, nondiscrete, totally disconnected field with a valuation). In particular, necessary and sufficient conditions for such an operator to be in the Schatten ideal \(C_ p\) are given. Reviewer: J.R.Holub MSC: 47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) 47B38 Linear operators on function spaces (general) Keywords:kernel; local field; Schatten ideal Citations:Zbl 0629.47023 PDFBibTeX XMLCite \textit{D. Timotin}, Stud. Math. 88, No. 1, 43--50 (1988; Zbl 0645.47016) Full Text: DOI EuDML