arXiv subjects

Sumit Parashar

Publications and source records attributed to Sumit Parashar.

3 recordsLinked to original sources

arXiv2026

Hausdorff operators and fractional Hausdorff operators in the Dunkl setting

In this paper, we investigate the boundedness properties of the Dunkl-type Hausdorff operator on generalized Dunkl-type Morrey spaces and generalized Dunkl-type Campanato spaces. Furthermore, we introduce the fractional Dunkl-type Hausdorff operator and study its boundedness from $L^p(\mathbb{R}, d\mu_\alpha)$ to $L^q(\mathbb{R}, d\mu_\alpha)$. We also establish the boundedness of the fractional Dunkl-type Hausdorff operator on generalized Dunkl-type Morrey spaces under suitable conditions. As a consequence of our main results, we derive several applications. Finally, we evaluate the exact norm of the Dunkl-type Hausdorff operator on Dunkl-type Morrey spaces and Dunkl-type Campanato spaces.

math.FA↗

arXiv2025

On the Boundedness of Generalized Fractional Integral Operators in Morrey Spaces and Camapanato Spaces associated with the Dunkl Operator on the Real line

It is known that the Dunkl-type fractional integral operator $I_\beta$ $(0 < \beta < 2\alpha + 2 =d_\alpha)$ is bounded from $L^p(\R,d\mu_\alpha)$ to $L^q (\R, d\mu_\alpha)$ when $1 < p < \frac{d_\alpha}{\beta}$ and $\frac{1}{p} - \frac{1}{q} = \frac{\beta}{d_\alpha}$. In \cite{spsa} , the authors introduced the generalized Dunkl-type fractional integral operator $T_\rho^\alpha$ and it's modified version $\tilde{T}_\rho^\alpha$ and extended the above boundedness results to the generalized Dunkl-type Morrey spaces and Dunkl-type $BMO_\phi$ spaces. In this paper we investigate the boundedness of generalized Dunkl-type fractional integral operators and it's modified version mainly on the Dunkl-type Campanato space.

math.FA↗

arXiv2025

Hardy-Littlewood maximal, generalized Bessel-Riesz and generalized fractional integral operators in generalized Morrey and $BMO_\phi$ spaces associated with Dunkl operator on the real line

The analysis of Morrey spaces, generalized Morrey spaces and $BMO_\phi$ spaces related to the Dunkl operators on $\mathbb{R}$ are covered in this paper. We prove the boundedness of the Hardy-Littlewood maximal operators, Bessel-Riesz operators, generalized Bessel-Riesz operators, and generalized fractional integral operators associated with Dunkl operators on $\mathbb{R}$ in the generalized Dunkl-type Morrey spaces. Further, we derive the boundedness of the modified version of the generalized fractional integral operators associated with the Dunkl operators on $\mathbb{R}$ in Dunkl-type $BMO_\phi$ spaces.

math.CA↗