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Salman Ashraf

Publications and source records attributed to Salman Ashraf.

6 recordsLinked to original sources
arXiv2026

Bilinear Calder\'{o}n-Zygmund operators on Vilenkin groups

In this article, we study bilinear Calder\'on--Zygmund operators on a Vilenkin group $G$. As a preliminary step, we establish a Grafakos--Torres-type endpoint weak-type result in our setting. Furthermore, we prove that such operators extend to bounded bilinear mappings from $L^{p_1}(G)\times L^{p_2}(G)$ into $L^p(G)$ under the natural condition $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}.$ We then obtain a corresponding boundedness result in Morrey spaces, showing that these operators extend to bounded bilinear mappings from $\mathcal{M}_{p_1,u_1}(G)\times \mathcal{M}_{p_2,u_2}(G)$ into $\mathcal{M}_{p,u}(G)$ under suitable assumptions. These results generalize the classical bilinear estimates to the setting of Vilenkin groups.

math.FA↗
arXiv2026

Boundedness of $p$-adic Hardy--Hilbert and Erd\'elyi--Kober fractional integral operators on $p$-adic Ces\`aro function Spaces

In this paper, we introduce Ces\`aro function spaces over $p$-adic fields and investigate their fundamental properties, such as the dilation operator and the Minkowski-type integral inequality. We establish boundedness result for $p$-adic Hardy--Hilbert-type integral operators acting on $p$-adic Ces\`aro function spaces, and as an application we derive $p$-adic analogue of the Hardy inequality, the Hilbert inequality, and the Hardy-Littlewood-P\'{o}lya inequality. Furthermore, we define the $p$-adic analogue of the Erd\'elyi--Kober fractional integral operators and prove their boundedness on $p$-adic Ces\`aro function spaces with the help of the obtained boundedness result.

math.FA↗
arXiv2025

Integral Operators on Generalized Weighted Central Morrey Spaces over Local Fields

We introduce generalised weighted central Morrey spaces over local fields and obtain a quantitative estimate for the boundedness of the Hardy--Hilbert-type integral operator on these newly introduced spaces, albeit specifically in the context of power-weighted spaces. A similar estimate is also obtained for the Hardy--Littlewood--Pólya operator.

math.FA↗
arXiv2023

Boundedness of $p$-adic Hardy-Hilbert type integral operator on Block spaces

In this paper, we estimate an operator norm of dilation operators on block spaces ($\mathfrak{B}_{r,α}(\mathbb{Q}_p)$) over $p$-adic field. With this estimate, we establish the boundedness of $p$-adic Hardy-Hilbert type integral operator on $\mathfrak{B}_{r,α}(\mathbb{Q}_p)$. Moreover as application to our result, we obtain the $p$-adic Hilbert inequality, $p$-adic Hardy inequality and $p$-adic Hardy-Littlewood-Pólya inequality on $\mathfrak{B}_{r,α}(\mathbb{Q}_p)$.

math.FA↗
arXiv2021

Dilation Operators in Besov Spaces over Local Fields

We consider a dilation operator on Besov spaces $(B^s_{r,t}(K))$ over local fields and estimate an operator norm on such a field for $s > σ_r = \text{max}\big(\frac{1}{r} -1,~0\big)$ which depends on the constant $k$ unlike the case of Euclidean spaces. In $\mathbb{R}^n$, it is independent of constant. A constant $k$ appears for liming case $s=0$ and $s=σ_r$. In case of local fields, the limig case is still open. Further we also estimate the localization property of Besov spaces over local fields.

math.FA↗