Geodesic
Hardy's inequality for a~magnetic Grushin operator with Aharonov--Bohm type magnetic field
Algebra i analiz, Tome 23 (2011) no. 2, pp. 1-8.

Voir la notice de l'article provenant de la source Math-Net.Ru

@article{AA_2011_23_2_a0,
     author = {L. Aermark and A. Laptev},
     title = {Hardy's inequality for a~magnetic {Grushin} operator with {Aharonov--Bohm} type magnetic field},
     journal = {Algebra i analiz},
     pages = {1--8},
     publisher = {mathdoc},
     volume = {23},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2011_23_2_a0/}
}
TY  - JOUR
AU  - L. Aermark
AU  - A. Laptev
TI  - Hardy's inequality for a~magnetic Grushin operator with Aharonov--Bohm type magnetic field
JO  - Algebra i analiz
PY  - 2011
SP  - 1
EP  - 8
VL  - 23
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2011_23_2_a0/
LA  - ru
ID  - AA_2011_23_2_a0
ER  - 
%0 Journal Article
%A L. Aermark
%A A. Laptev
%T Hardy's inequality for a~magnetic Grushin operator with Aharonov--Bohm type magnetic field
%J Algebra i analiz
%D 2011
%P 1-8
%V 23
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2011_23_2_a0/
%G ru
%F AA_2011_23_2_a0
L. Aermark; A. Laptev. Hardy's inequality for a~magnetic Grushin operator with Aharonov--Bohm type magnetic field. Algebra i analiz, Tome 23 (2011) no. 2, pp. 1-8. http://geodesic.mathdoc.fr/item/AA_2011_23_2_a0/

[1] Birman M. Sh.,, “O spektre singulyarnykh granichnykh zadach”, Mat. sb., 55(97):2 (1961), 125–174 | MR | Zbl

[2] D'Ambrozio L.,, “Nekotorye neravenstva Khardi na gruppe Geizenberga”, Differents. uravneniya, 40:4 (2004), 509–521 | MR

[3] D'Ambrosio L., “Hardy inequalities related to Grushin type operators”, Proc. Amer. Math. Soc., 132:3 (2004), 725–734 | DOI | MR

[4] Davies E. B., “A review of Hardy inequalities”, The Maz'ya Anniversary Collection (Rostock, 1998), v. 2, Oper. Theory Adv. Appl., 110, Birkhäuser-Verlag, Basel, 1999, 55–67 | MR | Zbl

[5] Dou J., Guo Q., Niu P., “Hardy inequalities with remainder terms for the generalized Baouendi–Grushin vector fields”, Math. Inequal. Appl., 13:3 (2010), 555–570 | MR | Zbl

[6] Garofalo N., “Unique continuation for a class of elliptic operators which degenerate on a manifold of arbitrary codimension”, J. Differential Equations, 104:1 (1993), 117–146 | DOI | MR | Zbl

[7] Garofallo N., Lanconelli E., “Frequency functions on Heisenberg group, the uncertainty principle and unique continuation”, Ann. Inst. Fourier (Grenoble), 40:2 (1990), 313–356 | MR

[8] Grushin V. V., “Ob odnom klasse gipoellipticheskikh operatorov”, Mat. sb., 83(125):3 (1970), 456–473 | MR | Zbl

[9] Kombe I., Hardy, Rellich and uncertainty principle inequalities on Carnot groups, Preprint, arXiv: math/0611850

[10] Laptev A., Weidl T., “Hardy inequalities for magnetic Dirichlet forms”, Mathematical Results in Quantum Mechanics (Prague, 1998), Oper. Theory Adv. Appl., 108, Birkhäuser, Basel, 1999, 299–305 | MR

[11] Mazya V. G., Prostranstva S. L. Soboleva, LGU, L., 1985 | MR

[12] Niu P., Chen Y., Han Y., “Some Hardy-type inequalities for the generalized Baouendi–Grushin operators”, Glasg. Math. J., 46:3 (2004), 515–527 | DOI | MR | Zbl

[13] Stein E. M., Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Math. Ser., 43, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl