## derivative of a function of time using its inverse fourier transform

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?

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You should give more context: where are the functions defined? What is assumed about these one? – Davide Giraudo Sep 25 at 15:30
functions are lipschits having compact support i.e. defined for a bounded interval of real line. – Hafiz ul Asad Sep 25 at 16:06
There are obvious bounds, like bounding the function by the integral of the absolute value of the Fourier transform. However, since that would be the level of homework, you must be looking for something less obvious. I suggest you make your question more precise. Until then, I am voting to close. – Michael Renardy Sep 25 at 17:44

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?