Abstract
In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator $I_{\rho}$ on the generalized weighted local Morrey spaces with $w^{q} \in A_{1+\frac{q}{p'}}$ for $1 \le p \le q \le \infty $ and including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le\infty$. We also prove the Adams-type boundedness of the operator $I_{\rho}$ on the generalized weighted Morrey spaces with $ w \in A_{p,q}$ for $1\le p\le q \le \infty$ and also including its the weak estimates with $w \in A_{1,q}$ for $1\le q\le \infty$.
Funding Statement
The research of Abdulhamit Kucukaslan was supported by the grant of The Scientific and Technological Research Council of Turkey, Grant TUBITAK-1059B191600675.
Version Information
The current pdf replaces the original pdf file, first available on 16 December 2021. The new version corrects the DOI prefix to read 10.32513.
Citation
Abdulhamit Kucukaslan. "Two-type estimates for the boundedness of generalized Riesz potential operator in the generalized weighted local Morrey spaces." Tbilisi Math. J. 14 (4) 111 - 134, December 2021. https://doi.org/10.32513/asetmj/1932200817
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