  In this article new bounds on weighted p-norms of ambiguity functions and
Wigner functions are derived. Such norms occur frequently in several areas of
physics and engineering. In pulse optimization for Weyl--Heisenberg signaling
in wide-sense stationary uncorrelated scattering channels for example it is a
key step to find the optimal waveforms for a given scattering statistics which
is a problem also well known in radar and sonar waveform optimizations. The
same situation arises in quantum information processing and optical
communication when optimizing pure quantum states for communicating in bosonic
quantum channels, i.e. find optimal channel input states maximizing the pure
state channel fidelity. Due to the non-convex nature of this problem the
optimum and the maximizers itself are in general difficult find, numerically
and analytically. Therefore upper bounds on the achievable performance are
important which will be provided by this contribution. Based on a result due to
E. Lieb, the main theorem states a new upper bound which is independent of the
waveforms and becomes tight only for Gaussian weights and waveforms. A
discussion of this particular important case, which tighten recent results on
Gaussian quantum fidelity and coherent states, will be given. Another bound is
presented for the case where scattering is determined only by some arbitrary
region in phase space.
