The Boundedness of Toeplitz-Type Operators on Vanishing-Morrey Spaces

Abstract

In this note, we prove that the Toeplitz-type Operator $\Theta_\alpha^b$ generated by the generalized fractional integral, Calderón-Zygmund operator and VMO function is bounded from $L^{p,\lambda} (R^n)$ to $L^{q,\mu} (R^n)$. We also show that under some conditions $\Theta_\alpha^b f \in  V L^{q,\mu} (B_R)$, the vanishing-Morrey space.