On the Boundedness of Generalized Fractional Integral Operators in Morrey Spaces and Camapanato Spaces associated with the Dunkl Operator on the Real line
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915605275213824 |
|---|---|
| author | Parashar, Sumit Adhikari, Saswata |
| author_facet | Parashar, Sumit Adhikari, Saswata |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Boundedness of Generalized Fractional Integral Operators in Morrey Spaces and Camapanato Spaces associated with the Dunkl Operator on the Real line Parashar, Sumit Adhikari, Saswata Functional Analysis 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. |
| title | On the Boundedness of Generalized Fractional Integral Operators in Morrey Spaces and Camapanato Spaces associated with the Dunkl Operator on the Real line |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2504.17241 |