Geodesic
On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces
Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 27-43

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In the paper we find conditions on the pair $(\omega _1,\omega _2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $\mathcal {M}_{p,\omega _1}$ to another $\mathcal {M}_{p,\omega _2}$, $1
In the paper we find conditions on the pair $(\omega _1,\omega _2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $\mathcal {M}_{p,\omega _1}$ to another $\mathcal {M}_{p,\omega _2}$, $1$, 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.
DOI : 10.21136/MB.2012.142786
Classification : 42B20, 42B25, 42B35
Keywords: generalized Morrey space; maximal operator; Hardy operator; singular integral operator 
Akbulut, Ali; Guliyev, Vagif; Mustafayev, Rza. On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces. Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 27-43. doi: 10.21136/MB.2012.142786
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