MATHEMATICA BOHEMICA, Vol. 137, No. 1, pp. 27-43, 2012

# On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

## Ali Akbulut, Vagif Guliyev, Rza Mustafayev

Ali Akbulut, Ahi Evran University, Department of Mathematics, Kirsehir, Turkey, e-mail: aakbulut@ahievran.edu.tr; Vagif Guliyev, Ahi Evran University, Department of Mathematics, Kirsehir, Turkey, Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, e-mail: vagif@guliyev.com; Rza Mustafayev, Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, e-mail: rzamustafayev@mail.az

Abstract: In the paper we find conditions on the pair $(\omega_1,\omega_2)$ which ensure the boundedness of the maximal operator and the Calderon-Zygmund singular integral operators from one generalized Morrey space $\mathcal{M}_{p,\omega_1}$ to another $\mathcal{M}_{p,\omega_2}$, $1<p<\infty$, and from the space $\mathcal{M}_{1,\omega_1}$ to the weak space $W\mathcal{M}_{1,\omega_2}$. As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.

Keywords: generalized Morrey space, maximal operator, Hardy operator, singular integral operator

Classification (MSC 2010): 42B20, 42B25, 42B35

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