Boundedness of the fractional maximal operator in generalized Morrey space on the Heisenberg group
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV Kırşehir Ahi Evran Üniversitesi, Türkiye
Yagub Y. Mammadov Azerbaijan National Academy Of Sciences, Azerbaycan
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Indian Journal of Pure and Applied Mathematics (Q4) | ||
| Dergi ISSN | 0019-5588 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 04-2013 |
| Cilt / Sayı / Sayfa | 44 / 2 / 185–202 | DOI | 10.1007/s13226-013-0010-2 |
| Makale Linki | https://link.springer.com/article/10.1007/s13226-013-0010-2 | ||
| Özet |
| In this paper we study the fractional maximal operator Mα, 0 ≤ α < Q on the Heisenberg group ℍn in the generalized Morrey spaces Mp, ϕ(ℍn), where Q = 2n + 2 is the homogeneous dimension of ℍn. We find the conditions on the pair (ϕ1, ϕ2) which ensures the boundedness of the operator Mα from one generalized Morrey space Mp, ϕ1(ℍn) to another Mq, ϕ2(ℍn), 1 < p < q < ∞, 1/p−1/q = α/Q, and from the space M1, ϕ1(ℍn) to the weak space WMq, ϕ2(ℍn), 1 < q < ∞, 1 − 1/q = α/Q. We also find conditions on the φ which ensure the Adams type boundedness of Mα from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{p,\phi ^{\tfrac{1} {p}} } \left( {\mathbb{H}_n } \right)$$\end{document} to … |
| Anahtar Kelimeler |
| fractional maximal function | generalized Morrey space | Heisenberg group | Schrödinger operator |
