given a general integral transform
$$ g(x)= \int_{0}^{\infty}dyf(y)K(xy) $$
for a general formula of the kernel $ K(xy) $ is there an inverse of the Integral transform to obtain $ f(x) $ from above
lets say that there will always be a function $ B$ so
$$ f(y)= \frac{1}{2\pi i} \oint_{C} dsB(ys)g(s) $$
as in the case of the inverse Laplace transform