What does $\hat{H}_D$ mean?

This is the transfer function of a differentiator, $\hat{H}_D(j \omega) = j\omega$. You can see it takes the derivative of a complex sinusoidal input voltage, as follows: if $\hat{V}_{\rm in} = \hat{V} e^{j\omega t}$, then the derivative is $\frac{d}{dt} \hat{V} e^{j\omega t}= j\omega \hat{V} e^{j \omega t} = j \omega \hat{V}_{\rm in}$. So taking the derivative is the same as multiplying by $j \omega$.