  We study the classical first-kind boundary integral equation reformulations
of time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and
sound-hard (Neumann) screens. We prove continuity and coercivity of the
relevant boundary integral operators (the acoustic single-layer and
hypersingular operators respectively) in appropriate fractional Sobolev spaces,
with wavenumber-explicit bounds on the continuity and coercivity constants. Our
analysis is based on spectral representations for the boundary integral
operators, and builds on results of Ha-Duong (Jpn J Ind Appl Math 7:489--513
(1990) and Integr Equat Oper Th 15:427--453 (1992)).
