Continuity in quasi-homogeneous Sobolev spaces for pseudo-differential operators with Besov symbols

In this paper a result of continuity for pseudo-differential operators With non-regular symbols on spaces of quasi-homogeneous type is given. More precisely, the symbols a(x, xi) take their values in a quasi-homogeneous Besov space with respect to the x variable; moreover a finite number of derivatives With respect to the second variable satisfies, in Besov norm, decay estimates of quasi-homogeneous type.