Cwikel type estimates for the bordered Airy transform

Abstract:

Compactness conditions as well as estimates for singular values of the bordered Airy transform $f\mathbb {A}g$ in $L_{2}(\mathbb {R})$ are studied for suitable functions $f(x)$, $g(x)$, $x\in \mathbb {R}$. Sufficient conditions for the operator $f\mathbb {A}g$ to be in the Schatten–von Neumann class $\mathfrak {S}_{p}$, $p\in (0,2)$, are obtained. In particular, certain conditions ensuring that the operator $f\mathbb {A}g$ is in trace class are given.