We investigate the Weyl calculus of pseudodifferential operators with the methods of time-frequency analysis. As symbol classes we use the modulation spaces, which are the function spaces associated to the short-time Fourier transform and the Wigner distribution. We investigate the boundedness and Schatten-class properties of pseudodifferential operators, and furthermore we study their mapping ...

We prove sharp estimates for the dilation operator f(x) 7−→ f(λx), when acting on Wiener amalgam spaces W (L, L). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces M, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

In this paper, we study the strongly singular integrals [Formula: see text] along homogeneous curves [Formula: see text]. We prove that [Formula: see text] is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces.

In this paper, we first prove the metric approximation property for weighted mixed-norm L (p1,...,pn) w spaces. Using Gabor frame representation, this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck’s theory becomes applicable, and we give criteria for nuclearity and r-nuclearity for operators acting on these spaces as well a...

We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct we obtain a characterization of all exponents p, q, r 1 , r 2 , t 1 , t 2 ∈ [1, ∞] of modulation sp...