What would be the bounds on the derivative of a function using its inverse fourier transform representation. Furthermore what would be the bounds on the absolute value of the function itself?



derivative of a function of time using its inverse fourier transform
The standard estimates are $|f(x)|$ is at most the $L^1$ norm of the Fourier transform,
and $|f'(x)|$ is at most the first moment of the Fourier transform. Is this what you are asking about?


