### Oscillatory integrals with variable Calderón-Zygmund kernel on vanishing generalized Morrey spaces

#### V. S. Guliyev, A. Ahmadli, S. E. Ekincioglu

In this paper, the authors investigate the boundedness of the oscillatory singular integrals with variable Calderón-Zygmund kernel on generalized Morrey spaces $M^{p,\varphi}(\Rn)$ and the vanishing generalized Morrey spaces $VM^{p,\varphi}(\Rn)$. When $1< p<\infty$ and $(\varphi_1,\varphi_2)$ satisfies some conditions, we show that the oscillatory singular integral operators $T_{\lambda}$ and $T_{\lambda}^{*}$ are bounded from $M^{p,\varphi_1}(\Rn)$ to $M^{p,\varphi_2}(\Rn)$ and from $VM^{p,\varphi_1}(\Rn)$ to $VM^{p,\varphi_2}(\Rn)$. Meanwhile, the corresponding result for the oscillatory singular integrals with standard Calderón-Zygmund kernel are established.

Tbilisi Mathematical Journal, Vol. 13(1) (2020), pp. 69-82