Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 1041-1054

POINCARÉ-TYPE INEQUALITIES IN MUSIELAK SPACES

Youssef Ahmida and Ahmed Youssfi

Sidi Mohamed Ben Abdellah University, National School of Applied Sciences
Laboratory of Engineering, Systems and Applications (LISA)
My Abdellah Avenue, Road Imouzer, P.O. Box 72 Fès-Principale, 30 000 Fez, Morocco; youssef.ahmida 'at' usmba.ac.ma

Abstract. In this paper we investigate Poincaré-type integral inequalities in the functional Musielak structure. We extend the ones already well known in Sobolev, Orlicz and variable exponent Sobolev spaces. We introduce conditions on the Musielak functions under which they hold. The identification with null trace functions space is given.

2010 Mathematics Subject Classification: Primary 46E30, 46E35, 26D10, 26D15, 46A80.

Key words: Musielak spaces, Poincaré-type inequalities, null trace functions space.

Reference to this article: Y. Ahmida and A. Youssfi: Poincaré-type inequalities in Musielak spaces. Ann. Acad. Sci. Fenn. Math. 44 (2019), 1041-1054.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4468