Appendix B: On the regularity of some integral kernels

We refer to an operator A in L²(Ω) possessing the features described by Eqs. (2.7), (2.8) or (2.9) (recall that the situation (2.7) is more general than (2.8), and (2.8) is more general than (2.9)). In this appendix we present a number of results which are useful in relation to several integral kernels associated to A. Proving these results would require a heavy use of functional analysis, which is not among the purposes of the present book; therefore, hereafter we just sketch the basic ideas that are presented with more details (and greater mathematical rigor) in [62]…