Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Javanshir J. Hasanov Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Stefan G. Samko Universidade Do Algarve, Portekiz
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Journal of Mathematical Analysis and Applications (Q1) | ||
| Dergi ISSN | 0022-247X Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 05-2013 |
| Cilt / Sayı / Sayfa | 401 / 1 / 72–84 | DOI | 10.1016/j.jmaa.2012.03.041 |
| Makale Linki | https://www.sciencedirect.com/science/article/pii/S0022247X12002454 | ||
| Özet |
| We consider local “complementary” generalized Morrey spaces [Formula: see text] in which the p-means of function are controlled over Ω∖B(x0,r) instead of B(x0,r), where Ω⊂Rn is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function ω(r) defining the “complementary” Morrey-type norm. In the case where ω is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy–Littlewood maximal operator and Calderon–Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type [Formula: see text] -theorem for the potential operators Iα(⋅), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities on ω(r), which do not assume any assumption on monotonicity of ω(r). |
| Anahtar Kelimeler |
| Fractional maximal operator | Generalized Morrey space | Local "complementary" Morrey spaces | Maximal operator | Riesz potential, singular integral operators, weighted spaces |
Science Direct
Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Google Scholar | 44 |
| Web of Science | 30 |