Riesz potential on the Heisenberg group and modified Morrey spaces
Yazarlar (2)
Prof. Dr. Vagıf GULIYEV
Kırşehir Ahi Evran Üniversitesi, Türkiye
Institute Of Mathematics And Mechanics Ministry Of Science And Education Republic Of Azerbaijan, Azerbaycan
| Makale Türü |
Özgün Makale
(SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale)
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| Dergi Adı | Analele Stiintifice Ale Universitatii Ovidius Constanta Seria Matematica (Q2) | ||
| Dergi ISSN | 1224-1784 Wos Dergi Scopus Dergi | ||
| Makale Dili | İngilizce | Basım Tarihi | 01-2012 |
| Cilt / Sayı / Sayfa | 20 / 1 / 189–212 | DOI | 10.2478/v10309-012-0013-8 |
| Makale Linki | https://sciendo.com/pdf/10.2478/v10309-012-0013-8 | ||
| 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 |
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| WoS | 5 |
| SCOPUS | 5 |