Nonlinear operations on a class of modulation spaces

الأصل · EN

We discuss when the nonlinear operation f F(f) maps the modulation space Mᵖ,qₛ(Rⁿ) (1 ≤ p,q ≤ ∞) to the same space again. It is known that Mᵖ,qₛ(Rⁿ) is a multiplication algebra when s > n-n/q, hence it is true for this space if F is entire. We claim that it is still true for non-analytic F when q≥4/3.