FRACTIONAL WEIGHTED SPHERICAL MEAN AND MAXIMAL INEQUALITY FOR THE WEIGHTED SPHERICAL MEAN AND ITS APPLICATION TO SINGULAR PDE
Yazarlar (3)
Istanbul Medeniyet University, Türkiye
Prof. Dr. Vagıf GULIYEV
Baku State University, Azerbaycan
Voronezhskiy Gosudarstvenniy Universitet, Rusya Federasyonu
| Makale Türü |
Özgün Makale
(SCOPUS dergilerinde yayınlanan tam makale)
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| Dergi Adı | Journal of Mathematical Sciences United States | ||
| Dergi ISSN | 1072-3374 Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 10-2022 |
| Cilt / Sayı / Sayfa | 266 / 5 / 744–764 | DOI | 10.1007/s10958-022-06099-x |
| Makale Linki | https://link.springer.com/content/pdf/10.1007/s10958-022-06099-x.pdf | ||
| Özet |
| In this paper we establish a mean value property for the functions which is satisfied to Laplace–Bessel equation. Our results involve the generalized divergence theorem and the second Green’s identities relating the bulk with the boundary of a region on which differential Bessel operators act. Also we design a fractional weighted mean operator, study its boundedness, obtain maximal inequality for the weighted spherical mean and get its boundedness. The connection between the boundedness of the spherical maximal operator and the properties of solutions of the Euler–Poisson–Darboux equation with Bessel operators is given as an application. |
| Anahtar Kelimeler |
| B-harmonic function | Bessel operator | Fractional weighted mean | Laplace–Bessel operator | Maximal inequality | Singular Euler–Poisson–Darboux equation |