Riesz potential in generalized Morrey spaces on the Heisenberg group

被引：1
作者：
Guliyev V.S. [1 ,2 ,4 ]
Eroglu A. [3 ]
Mammadov Y.Y. [2 ,4 ,5 ]
机构：
[1] Ahi Evran University, Kirsehir
[2] Institute of Mathematics and Mechanics, Baku, AZ 1141, Azerbaijan NAS 9, F. Agaev St.
[3] Nigde University, Nigde
[4] Institute of Mathematics and Mechanics, Baku, AZ 1141, Azerbaijan NAS 9, F. Agaev St.
[5] Nakhchivan Teacher-Training Institute, Nakhchivan
来源：
Journal of Mathematical Sciences | 2013年 / 189卷 / 3期
关键词：
Heisenberg Group; Besov Space; Azerbaijan; Morrey Space; Riesz Potential;
D O I：
10.1007/s10958-013-1193-0
中图分类号：
学科分类号：
摘要：
We consider the Riesz potential operator Iα, on the Heisenberg group Hn in generalized Morrey spaces Mp,φ(Hn) and find conditions for the boundedness of Iα as an operator from Mp,φ1(Hn) to Mp,φ2(Hn), 1 < p < ∞, and from Mp,φ1(Hn) to a weak Morrey space WM1,φ2(Hn). The boundedness conditions are formulated it terms of Zygmund type integral inequalities. Based on the properties of the fundamental solution of the sub-Laplacian on Hn, we prove two Sobolev-Stein embedding theorems for generalized Morrey and Besov-Morrey spaces. Bibliography: 40 titles. © 2013 Springer Science+Business Media New York.
引用
收藏
页码：365 / 382
页数：17
相关论文
共 40 条
  • [1] Folland G.B., Stein E.M., Spaces on Homogeneous Groups, (1982)
  • [2] Garofalo N., Lanconelli E., Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation, Atin. Inst. Fourier, Grenoble, 40, pp. 313-356, (1990)
  • [3] Stein E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, (1993)
  • [4] Hormander L., Hypoelliptic second order differential equations, Acta Math., 119, pp. 147-171, (1967)
  • [5] Folland G.B., Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat., 13, pp. 161-207, (1975)
  • [6] Xiao J., He J., Riesz potential on the Heisenberg group, J. Inequal. Appl., 2011, (2011)
  • [7] Morrey C.B., On the solutions of quasi-linear elliptic partial differential equations, Am. Math. Soc., 43, pp. 126-166, (1938)
  • [8] Mazzucato A.L., Besov-Morrey spaces: function space theory and applications to nonlinear PDE, Trans. Amer. Math. Soc., 355, pp. 1297-1364, (2003)
  • [9] Taylor M.E., Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations, Commun. Partial Differ. Equ., 17, pp. 1407-1456, (1992)
  • [10] Perez C., Two weighted norm inequalities for Riesz potentials and uniform L<sub>p</sub>-weighted Sobolev inequalities, Indiana Univ. Math. J., 39, pp. 31-44, (1990)
1234