Tikhonov Regularization can be described as
$$ \min_g \| Yg - x\|_2^2 + \alpha \|g\|_2^2 $$
and LASSO can be described as:
$$ \min_g \| Yg - x\|_2^2 + \beta \|g\|_1 $$
Is there any way to relate the resulting error (e.g. mean squared error) between these two?
The answer depends on $Y$, $x$, $\alpha$ and $\beta$ but is there anything that can be said if either of these have certain forms?