BOUNDEDNESS OF THE MAXIMAL, POTENTIAL AND SINGULAR OPERATORS IN THE GENERALIZED VARIABLE EXPONENT MORREY SPACES
Yazarlar (3)
Prof. Dr. Vagıf GULIYEV Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Javanshir J. Hasanov
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
Stefan G. Samko
Universidade Do Algarve, Portekiz
Universidade Do Algarve, Portekiz
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
|
||
| Dergi Adı | Mathematica Scandinavica (Q3) | ||
| Dergi ISSN | 0025-5521 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2010 |
| Cilt / Sayı / Sayfa | 107 / 2 / 285–304 | DOI | 10.7146/math.scand.a-15156 |
| Makale Linki | https://scholar.google.com/scholar?cluster=12794287413632331124&hl=en&oi=scholarr | ||
| Özet |
| We consider generalized Morrey spaces 𝓜p(·),ω(Ω) with variable exponent p(x) and a general function ω(x, r) defining the Morrey-type norm. In case of bounded sets Ω ⊂ Rn 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-Adams type 𝓜p(·),ω(Ω) → 𝓜q(·),ω(Ω)-theorem for the potential operators Iα(·), also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral integral inequalities on ω(x, r), which do not assume any assumption on monotonicity of ω(x, r) in r. |
| Anahtar Kelimeler |