essentially bounded function in a sentence

1. The induced operator is bounded if and only if the coefficients of the Toeplitz matrix A are the Fourier coefficients of some essentially bounded function f.
2. Similarly one can form the space of essentially bounded functions, with the norm given by the essential supremum, and the positive elements of the dual of this space are given by bounded contents that vanish on sets of measure 0.
3. It's difficult to find essentially bounded function in a sentence.