LAUSR

In this paper, the authors introduce and investigate a certain family of pseudo‐differential operators which is associated with the symbol class Sωr$$ {S}_{\omega}^r $$ on the space Sωℝ+n+1$$ {S}_{\omega}\left({\mathbb{R}}_{+}^{n+1}\right) $$ for a real‐valued convex function ω$$ \omega $$ . By appealing to the theory of the Weinstein transform, various properties of the pseudo‐differential operator 𝒜(x,D) associated with the symbol class SMr,l$$ {S}_M^{r,l} $$ are discussed. The representation of the pseudo‐differential operator 𝒜(x,D) associated with the indicatrix M(t)$$ M(t) $$ is also obtained. Finally, the L2$$ {L}^2 $$ ‐norm of the pseudo‐differential operator 𝒜(x,D) with the indicatrix M(t)$$ M(t) $$ and the function ω(t)$$ \omega (t) $$ is investigated.