| Yazarlar |
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi |
Yagub Y. Mammadov
|
| Özet |
| In this paper we study the fractional maximal operator M-alpha, 0 <= alpha < Q and the Riesz potential operator F-alpha L 0 < alpha < Q on the Heisenberg group in the modified Morrey spaces L-p,L-lambda(H-n), where Q = 2n + 2 is the homogeneous dimension on H-n. We prove that the operators M-alpha and F-alpha are bounded from the modified Morrey space <(L)over tilde>(1,lambda)(H-n) to the weak modified Morrey space W (L) over tilde (q,lambda) (H-n) if and only if, alpha/Q <= 1 - 1/q <= alpha/(Q - lambda) and from (L) over tilde (p,lambda)(H-n) to (L) over tilde (q,lambda)(H-n) if and only if, alpha/Q <= 1/p - 1/q <= alpha/(Q - lambda). In the limiting case Q-lambda/alpha <= p <= Q/alpha we prove that the operator M-alpha is bounded from (L) over tilde (p,lambda)(H-n) to L-infinity (H-n) and the modified fractional integral operator (I) over tilde (alpha) is bounded from (L) over tilde (p,lambda)(H-n) to BMO(H-n). As applications of the properties of the fundamental solution of sub-Laplacian L on H-n, we prove two Sobolev-Stein embedding theorems on modified Morrey and Besov-modified Morrey spaces in the Heisenberg group setting. As an another application, we prove the boundedness of F alpha, from the Besov-modified Morrey spaces B (L) over tilde (s)(p theta),(lambda)(H-n) to B (L) over tilde (s)(q theta),lambda(H-n). |
| Anahtar Kelimeler |
| BMO space | Fractional integral | Fractional maximal function | Heisenberg group | Modified Morrey space | Riesz potential |
| Makale Türü | Özgün Makale |
| Makale Alt Türü | SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale |
| Dergi Adı | ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA |
| Dergi ISSN | 1224-1784 |
| Dergi Grubu | Q2 |
| Makale Dili | İngilizce |
| Basım Tarihi | 01-2012 |
| Cilt No | 20 |
| Sayı | 1 |
| Sayfalar | 189 / 212 |
| Doi Numarası | 10.2478/v10309-012-0013-8 |
| Atıf Sayıları | |
| WoS | 3 |
| SCOPUS | 3 |
