ABSTRACT
The first two questions wil l be considered within the frameworks of convergence in Zp-norms (see Sections 1 and 3), the final results being given in Theorems 5.11 and 5.12.
Later, in Chapter 6, we shall investigate the convergence of hypersingular integrals with more general characteristics, not necessarily stabilizing at the origin and infinity, but we find it convenient to treat this more general case after the detailed investigation of some spaces L% r(R
n) of fractional smoothness, connected with the convergence of hypersingular integrals. Nevertheless, we touch on the idea of such spaces in this chapter while taking f € Lr and considering the convergence of the integral (5.1) in Lp with different values of p and r.
