Wiener-Hopf integral operators

Throughout this chapter we let L P and L + p (1≤P≤∞) refer to the L P spaces of Lebesgue measure on ℝ and ℝ+, respectively. The L p spaces on the unit circle will be denoted by L P (T). The operator P defined by P:L p →L p +, φ ↦ φ | ℝ+is clearly bounded for 1 ≤ p ≤ ∞.