The structure of bandlimited BMO-functions and applications

In this paper we analyze the structure of bandlimited BMO-functions. Using a recently found equation for the calculation of the Hilbert transform of bounded bandlimited functions, we derive a decomposition result for bandlimited BMO-functions, which is similar to the well-known Fefferman–Stein decomposition. Based on this decomposition we characterize the range of the Hilbert transform. Moreover, we present interesting applications of this result. We characterize the peak value behavior of bandlimited BMO-functions, show that the derivative of bandlimited BMO-functions is bounded, and prove a sampling theorem for bandlimited BMO-functions.