Multidimensional case: radial functions

Of course, the approach elaborated in Part I plays a good part in the extension in the previous chapters of this second part. However, there is one more particular setting that can be treated immediately. Using a formula for the Fourier transform of a radial function from [139] (see also [92, Ch.4]), we can generalize the obtained above results to the radial case. Before doing this, we not only present certain needed preliminaries but also give a general necessary condition for the integrability of the Fourier transform. It is not for just radial functions, quite the contrary, it is also for general functions, but it is given in terms of the radial part of the given function. Also, a certain notion from Part I is used to provide terms for the formulation of a necessary condition. The latter also relates this to functions of bounded variation, though formally the obtained necessary condition does not claim for any assumption concerning variation.