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Saswata Adhikari

Publications and source records attributed to Saswata Adhikari.

7 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 $L^p(\mathbb{R}, dμ_α)$ to $L^q(\mathbb{R}, dμ_α)$. 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↗
arXiv2026

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 $I_β$ $(0 < β< 2α+ 2 =d_α)$ is bounded from $L^p(\R,dμ_α)$ to $L^q (\R, dμ_α)$ when $1 < p < \frac{d_α}β$ and $\frac{1}{p} - \frac{1}{q} = \fracβ{d_α}$. In \cite{spsa} , the authors introduced the generalized Dunkl-type fractional integral operator $T_ρ^α$ and it's modified version $\tilde{T}_ρ^α$ and extended the above boundedness results to the generalized Dunkl-type Morrey spaces and Dunkl-type $BMO_ϕ$ 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↗
arXiv2026

Adams type Dunkl Stein-Weiss inequality on Dunkl Morrey spaces on the real line

In this paper, we study the weighted boundedness of the Dunkl fractional integral operator (i.e., Dunkl Stein-Weiss inequality) associated with the Dunkl operator on $\mathbb{R}$. Indeed, we obtain the Adams-type Dunkl Stein-Weiss inequality on Dunkl-Morrey spaces. Our result extends the classical Adams type Stein-Weiss inequality on Morrey space result to the Dunkl setting. Furthermore, we establish the weighted boundedness of the Dunkl fractional maximal function on Dunkl Morrey spaces.

math.CA↗
arXiv2025

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

The analysis of Morrey spaces, generalized Morrey spaces and $BMO_ϕ$ 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 $BMO_ϕ$ spaces.

math.CA↗
arXiv2017

Left Translates of a Square Integrable Function on the Heisenberg group

The aim of this paper is to study some properties of left translates of a square integrable function on the Heisenberg group. First, a necessary and sufficient condition for the existence of the canonical dual to a function $φ\in L^{2}(\mathbb{R}^{2n})$ is obtained in the case of twisted shift-invariant spaces. Further, characterizations of $\ell^{2}$-linear independence and the Hilbertian property of the twisted translates of a function $φ\in L^{2}(\mathbb{R}^{2n})$ are obtained. Later these results are shown in the case of the Heisenberg group.

math.FA↗
arXiv2017

Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg group

Let $E(\mathscr{A})$ denote the shift-invariant space associated with a countable family $\mathscr{A}$ of functions in $L^{2}(\mathbb{H}^{n})$ with mutually orthogonal generators, where $\mathbb{H}^{n}$ denotes the Heisenberg group. The characterizations for the collection $E(\mathscr{A})$ to be orthonormal, Bessel sequence, Parseval frame and so on are obtained in terms of the group Fourier transform of the Heisenberg group. These results are derived using such type of results which were proved for twisted shift-invariant spaces and characterized in terms of Weyl transform. In the last section of the paper, some results on oblique dual of the left translates of a single function $φ$ is discussed in the context of principal shift-invariant space $V(φ)$.

math.FA↗