Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 403-426

SOBOLEV AND TRUDINGER TYPE INEQUALITIES ON GRAND MUSIELAK–ORLICZ–MORREY SPACES

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno and Tetsu Shimomura

4-24 Furue-higashi-machi, Nishi-ku, Hiroshima 733-0872, Japan; fymaeda 'at' h6.dion.ne.jp

Hiroshima Institute of Technology, Department of Mechanical Systems Engineering
2-1-1 Miyake Saeki-ku Hiroshima 731-5193, Japan; y.mizuta.5x 'at' it-hiroshima.ac.jp

Oita University, Faculty of Education and Welfare Science
Dannoharu Oita-city 870-1192, Japan; t-ohno 'at' oita-u.ac.jp

Hiroshima University, Graduate School of Education, Department of Mathematics
Higashi-Hiroshima 739-8524, Japan; tshimo 'at' hiroshima-u.ac.jp

Abstract. Our aim in this paper is to establish generalizations of Sobolev's inequality and Trudinger's inequality for general potentials of functions in grand Musielak–Orlicz–Morrey spaces.

2010 Mathematics Subject Classification: Primary 31B15, 46E35.

Key words: Riesz potentials, maximal functions, Sobolev's inequality, Trudinger's inequality, grand Musielak–Orlicz–Morrey spaces.

Reference to this article: F.-Y. Maeda, Y. Mizuta, T. Ohno and T. Shimomura: Sobolev and Trudinger type inequalities on grand Musielak–Orlicz–Morrey spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 403-426.

Full document as PDF file

doi:10.5186/aasfm.2015.4027