Open Access

Weighted Variable Exponent Sobolev spaces on metric measure spaces


Cite

[1] Adams, D.R. and Hedberg, L.I. Function spaces and potential theory, Springer (1999).Search in Google Scholar

[2] Aissaoui, N. and Benkirane, A. Capacité dans les epaces d’Orlicz, Ann. Sci. Math. Québec18 (1) (1994), 1 - 23.Search in Google Scholar

[3] Aissaoui, N. and Benkirane, A. Potentiel non lineaire dans les espaces d’Orlicz. Ann. Sci. Math. Québec18 (2) (1994), 105 - 118.Search in Google Scholar

[4] N. Aissaoui, Strongly nonlineaire potentiel, Abstract and Applied Analysis, 2002, 357-374.10.1155/S1085337502203024Search in Google Scholar

[5] David Cruz-Uribe , Lars Diening, HÄSTÖ. The maximal operator on weighted variable Lebesgue spaces, Georgian Mathematical Journal 15(4) ů January (2008).Search in Google Scholar

[6] Diening, L., Harjulehto, P., HÄSTÖ, P. and Rudicka, M. Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Mathematics, vol, 2017. Springer, Berlin (2011).10.1007/978-3-642-18363-8Search in Google Scholar

[7] P. Hajlasz, Sobolev space on arbitry metric space, Kluwer academic publishers, 1996, 403-415.Search in Google Scholar

[8] M.C. Hassib, Y. Akdim, N. Aissaoui and. Musielak-Orlicz-Sobolev spaces on arbitrary metric space. Commentationes Mathematicae. vol.Search in Google Scholar

[9] P. Harjulehto, P. HÄSTÖ and M. Pere, Variable exponent Lebesgue spaces on metric spaces, the Hardy- Littlewood maximal operator, Real Anal. Exchange 30 (2005), no. 1, 87-104.Search in Google Scholar

[10] Ismail Aydin. Journal of Function Spaces and Applications. Volume 2012, 17 pages.10.1155/2012/132690Search in Google Scholar

[11] J. Kinnunen and O.Martio, The Soboleve capacity on metric spaces, Annales Academic Scientiarum Fennicae, 1996, 367-382.Search in Google Scholar

[12] E. J. McShane, Extension of range of functions, Bull. Am. Math. Soc, 1934, 837-842.10.1090/S0002-9904-1934-05978-0Search in Google Scholar

[13] Ismail Aydin. Journal of Function Spaces and Applications. Volume 2012, 17 pages.10.1155/2012/132690Search in Google Scholar

[14] T. Kilpeläinen, J. Kinnunen, and O. Martio, Sobolev spaces with zero boundary values on metric spaces, Potential Analysis, 12 (2000), 233-247.10.1023/A:1008601220456Search in Google Scholar

[15] Petteri Harjulehto, Peter Hasto and Mikko Pere. Variable exponent Sobolev spaces on metric measure spaces, Funct. Approx. Comment. Math.36, 2006, 79-94.10.7169/facm/1229616443Search in Google Scholar

[16] Takao Ohno and Tetsu Shimomura. Musielak-Orlicz-Sobolev spaces on metric measure spaces. Czechoslovak mathematical journal, Volume 65, (2015), Issue 2, pp 435-474.10.1007/s10587-015-0187-0Search in Google Scholar