Somewhat imprecisely, the Riesz transforms of formula_7 give the first partial derivatives of a solution of the equation  where Δ is the Laplacian. Thus the Riesz transform of formula_7 can be written as:  In particular, one should also have so that the Riesz transforms give a way of recovering information about the entire Hessian of a function from knowledge of only its Laplacian. This is now made more precise. Suppose that formula_12 is a Schwartz function. Then indeed by the explicit form of the Fourier multiplier, one has  The identity is not generally true in the sense of distributions. For instance, if "formula_12" is a tempered distribution such that formula_15, then one can only conclude that  for some polynomial formula_17.