Maximal, Potential, and Singular Operators in the Generalized Variable Exponent Morrey Spaces on Unbounded Sets
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Universidade Do Algarve, Portekiz
| 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 | 08-2013 |
| Cilt / Sayı / Sayfa | 193 / 2 / 228–248 | DOI | 10.1007/s10958-013-1449-8 |
| Makale Linki | https://link.springer.com/content/pdf/10.1007/s10958-013-1449-8.pdf | ||
| Özet |
| We consider generalized Morrey spaces Mp(·),ω(·)(Ω) with a variable exponent p(x) and a general function ω(x, r) defining a Morrey type norm. We extend the results obtained earlier for bounded sets Ω ⊂ ℝn by proving the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular operators with standard kernels in Mp(·),ω(·)(Ω). We prove a Sobolev type Mp(·),ω1(·)(Ω) → Mq(·),ω2(·)(Ω)-theorem, both the Spanne and Adams versions, for potential operators I α(·), where α(x) can be variable even if Ω is unbounded. The boundedness conditions are formulated either in terms of Zygmund type integral inequalities on ω(x, r) or in terms of supremal operators. Bibliography: 36 titles. © 2013 Springer Science+Business Media New York. |
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