The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces (Analysis in Theory and Applications, 2011)
In this note, we prove that the Toeplitz-type Operator $Θ_α^b$ generated by the generalized fractional integral, Calderón-Zygmund operator and VMO function is bounded from $L^{p,λ} (R^n)$ to $L^{q,μ} (R^n)$. We also show that under some conditions $Θ_α^b f \in V L^{q,μ} (B_R)$, the vanishing-Morrey space.
Keywords: Toeplitz-type operator; generalized fractional integral; vanishing-Morrey space.