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\(C_ p\)-estimates for certain kernels on local fields. (English) Zbl 0645.47016

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)

Citations:

Zbl 0629.47023
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