Let Y be a locally convex vector space with a Gaussian Radon measureγ denote by A(Y) and (y), two spaces of test functions on Y, and denote byμ(Y) and με(y), two spaces of distributions on Y. We prove that A(Y) (or(the symbol "*" means the complex conjugate operation). Using this embedding theorem we give a direct formula forFourier transform of h∈L2(Y, γ) as a distributions on Y. Moreover, by this embeddingtheorem we prove that infinite dimensional pseudodifferential operator A on A(Y) (orε(Y)) is continuous ω.r.t the norm of L2(Y, γ) if and only if for the adjoint operatorA' of A, we have A'(L'(Y, γ)) L2(Y, γ).
Fu Zhou GONG,Zhao DONG.
An Embedding Theorem for Space of Distributions on Locally Convex Space. Acta Mathematica Sinica, Chinese Series, 1999, 42(2) https://doi.org/10.12386/A1999sxxb0039