Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 563-577

VARIABLE EXPONENT WEIGHTED NORM INEQUALITY FOR GENERALIZED RIESZ POTENTIALS

Fumi-Yuki Maeda, Yoshihiro Mizuta and Tetsu Shimomura

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

4-13-11 Hachi-Hon-Matsu-Minami, Higashi-Hiroshima 739-0144, Japan; yomizuta 'at' hiroshima-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 variable exponent weighted norm inequalities for generalized Riesz potentials via norm inequalities in non-homogeneous central Herz–Morrey spaces.

2010 Mathematics Subject Classification: Primary 46E30, 31B15.

Key words: Weighted norm inequality, variable exponent, Sobolev's inequality, Riesz potentials.

Reference to this article: F.-Y. Maeda, Y. Mizuta and T. Shimomura: Variable exponent weighted norm inequality for generalized Riesz potentials. Ann. Acad. Sci. Fenn. Math. 43 (2018), 563-577.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4336