Boundedness of multilinear pseudo-differential operators of 𝑆_0,0-type in 𝐿²-based amalgam spaces

Abstract

We consider the multilinear pseudo-differential operators with symbols in a generalized 𝑆_0,0-type class and prove the boundedness of the operators from (𝐿², ℓ^{𝑞₁}) ×⋯ ×(𝐿², ℓ^{𝑞_𝑁}) to (𝐿², ℓ^𝑟), where (𝐿², ℓ^𝑞) denotes the 𝐿²-based amalgam space. This extends the previous result by the same authors, which treated the bilinear pseudo-differential operators and gave the 𝐿² ×𝐿² to (𝐿², ℓ¹) boundedness.