Abstract
We consider various embedding theorems for Sobolev-type function classes with variable integrability exponent on a metric space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kovacik O. and Rakosnik J., “In spaces L p(x) and W k,p(x),” Czechoslovak Math. J., 41, No. 4, 592–618 (1991).
Haj’asz P., “Sobolev spaces on an arbitrary metric spaces,” Potential Anal., 5, No. 4, 403–415 (1996).
Sobolev met Poincaré, Amer Math. Soc., Providence, RI (2000) (Mem. Amer. Math. Soc.; V. 145, No. 688).
Haj’asz P. and Martio O., “Traces of Sobolev functions on fractal type sets and characterization of extension domains,” J. Funct. Anal., 143, No. 1, 221–246 (1997).
Romanov A. S., “On the traces of Sobolev functions on the boundary of a cusp with a Hölder singularity,” Siberian Math. J., 48, No. 1, 176–184 (2007).
Edmunds D. and Rákosník J., “Sobolev embeddings with variable exponent,” Studia Math., 143, No. 3, 267–293 (2000).
Sharapudinov I. I., “Topology of the space L p(t)([0, 1]),” Math. Notes, 26, No. 4, 796–806 (1979).
Harjulehto P., Hästö P., and Pere M., “Variable exponent Lebesgue spaces on metric spaces: The Hardy-Littlewood maximal operator,” Real Anal. Exchange, 30, No. 1, 87–104 (2004/2005).
Adamowicz T., Harjulehto P., and Hästö P., “Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces,” http://www.helsinki.fi/pharjule/varsob/pdf/maximal-submitted.pdf).
Strömberg J.-O. and Torchinsky A., Weighted Hardy Spaces, Springer-Verlag, Berlin etc. (1989) (Lecture Notes in Math., 1381).
Romanov A. S., “Traces of functions of generalized Sobolev classes,” Siberian Math. J., 48, No. 4, 678–693 (2007).
Federer H., Geometric Measure Theory, Springer-Verlag, New York (1969).
Haj’asz P. and Kinnunen J., “Hölder quasicontinuity of Sobolev functions on metric spaces,” Rev. Mat. Iberoamericana, 14, No. 3, 601–622 (1998).
Romanov A. S., “Embedding theorems for generalized Sobolev spaces,” Siberian Math. J., 40, No. 4, 931–937 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text Copyright © 2014 Romanov A.S.
The author was supported by Integration Project No. 56 of the Far Eastern and Siberian Divisions of the Russian Academy of Sciences.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 1, pp. 178–194, January–February, 2014.
Rights and permissions
About this article
Cite this article
Romanov, A.S. Sobolev-type functions with variable integrability exponent on metric measure spaces. Sib Math J 55, 142–155 (2014). https://doi.org/10.1134/S0037446614010170
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446614010170