Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 721-744

SOME NORM INEQUALITIES IN MUSIELAK-ORLICZ SPACES

Fumi-Yuki Maeda, Yoshihiro Sawano and Tetsu Shimomura

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

Tokyo Metropolitan University, Department of Mathematics and Information Sciences
Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan; ysawano 'at' tmu.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 various norm inequalities in Musielak-Orlicz spaces. We give a generalization of a result due to Cruz-Uribe, Fiorenza, Martell and Pérez and apply it to obtain norm inequalities for classical operators as well as an Olsen inequality in Musielak-Orlicz spaces.

2010 Mathematics Subject Classification: Primary 26A33, 42B25, 42B35, 41A17.

Key words: Musielak-Orlicz space, Riesz potential, weighted inequality, singular integral operator, Kerman-Sawyer inequality, Olsen inequality.

Reference to this article: F.-Y. Maeda, Y. Sawano and T. Shimomura: Some norm inequalities in Musielak-Orlicz spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 721-744.

Full document as PDF file

doi:10.5186/aasfm.2016.4148