Boundedness of maximal, potential type, and singular integral operators in the generalized variable exponent Morrey type spaces
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Azerbaijan National Academy Of Sciences, Azerbaycan
Universidade Do Algarve, Portekiz
| Makale Türü |
Özgün Makale
(SCOPUS dergilerinde yayınlanan tam makale)
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| Dergi Adı | Journal of Mathematical Sciences | ||
| Dergi ISSN | 1072-3374 Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 10-2010 |
| Cilt / Sayı / Sayfa | 170 / 4 / 423–443 | DOI | 10.1007/s10958-010-0095-7 |
| Makale Linki | https://link.springer.com/content/pdf/10.1007/s10958-010-0095-7.pdf | ||
| Özet |
| We consider generalized Morrey type spaces Mp(·), θ(·), ω(·) (ω)with variable exponents p(x), θ(r) and a general function ω(x, r) defining a Morrey type norm. In the case of bounded sets ω ⊂ ℝn, we prove the boundedness of the Hardy-Littlewood maximal operator and Calderón-Zygmund singular integral operators with standard kernel. We prove a Sobolev-Adams type embedding theorem Mp(·), θ1(·), ω1(·) (ω) → Mp(·), θ2(·), ω2(·) (ω) for the potential type operator Iα(·) of variable order. In all the cases, we do not impose any monotonicity type conditions on ω(x, r) with respect to r. Bibliography: 40 titles. © 2010 Springer Science+Business Media, Inc. |
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