We show that multilinear pseudodifferential operators with symbols in the modulation space M are bounded on products of modulation spaces. In particular, M includes non-smooth symbols. Several… (More)

Árpad Bényi1, Diego Maldonado2, Andrea R. Nahmod3, and Rodolfo H. Torres∗4 1 Department of Mathematics, Western Washington University, Bellingham, WA 98225-9063, USA 2 Department of Mathematics,… (More)

We define homogeneous classes of x-dependent anisotropic symbols Ṡ γ,δ(A) in the framework determined by an expansive dilation A, thus extending the existing theory for diagonal dilations. We revisit… (More)

We characterize triples of cevians which form a triangle independent of the triangle where they are constructed. This problem is equivalent to solving a three-parameter family of inequalities which… (More)

We prove the boundedness of a general class of Fourier multipliers, in particular of the Hilbert transform, on modulation spaces. In general, however, the Fourier multipliers in this class fail to be… (More)

Hilbert’s proof, apart from the determination of the best possible constant π csc(π/p), was published by Weyl [7]. The calculation of the constant, and the integral analogue of Hilbert’s double… (More)

We use the theory of Gabor frames to prove the boundedness of bilinear pseudodifferential operators on products of modulation spaces. In particular, we show that bilinear pseudodifferential operators… (More)

We consider the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS) : i∂tu+Δu = ±|u|2u on Rd, d ≥ 3, with random initial data and prove almost sure well-posedness results below the… (More)