One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908556461080576 |
|---|---|
| author | Rubin, Boris |
| author_facet | Rubin, Boris |
| contents | We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a spherical cap. In the case $n=2$, this problem arises in electrostatics, elasticity, and some other applied areas. The main tools are stereographic projection, hypersingular integrals of the Marchaud type, Poisson integrals, and spherical harmonic decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap Rubin, Boris Functional Analysis 31B10, 45P05, 47G40 We introduce fractional integrals on the $n$-dimensional spherical cap, study their boundednes in weighted $L^p$ spaces and obtain explicit inversion formulas. The results are applied to the inversion problem for Riesz potentials on a spherical cap. In the case $n=2$, this problem arises in electrostatics, elasticity, and some other applied areas. The main tools are stereographic projection, hypersingular integrals of the Marchaud type, Poisson integrals, and spherical harmonic decompositions. |
| title | One-sided Fractional Integrals and Riesz Potentials on a Spherical Cap |
| topic | Functional Analysis 31B10, 45P05, 47G40 |
| url | https://arxiv.org/abs/2509.19584 |