ON TRUNCATED WIENER-HOPF OPERATORS AND BMOpZq

whenever Φ is such that this extends to a bounded operator on Lpr0, asq. Whenever a is of no importance we will omit it from the notation. We abbreviate by saying that WΦ is a TWH-operator. These operators (or rather, unitarily equivalent ones) also go under the name finite interval convolution operators, truncated Hankel operators or Toeplitz operators on the Paley-Wiener space. See e.g. [1, 2, 8, 9] and [10]. We will in this paper see that the properties of TWH-operators are more similar to those of Hankel operators rather than Toeplitz operators. Let F denote the Fourier transform on LpRq, defined as follows: