$\int_0^{a}ds dv (v s)^{K+n-1}(\frac{d}{d(sv)})^k\delta(2sv-s)$
is it right to obtain
$\int_0^{a}ds dv (v s)^{K+n-1}(\frac{1}{s})^k(\frac{d}{d(v)})^k\frac{1}{2s}\delta(v-1/2)=\int_0^{a}ds \frac{( s)^{n-2}}{2}(\frac{d}{dv})^k\Bigg[(v)^{k+n-1}\Bigg] _{v=1/2}$