Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 405-420

APPROXIMATE IDENTITIES AND YOUNG TYPE INEQUALITIES IN VARIABLE LEBESGUE-ORLICZ SPACES L^p(.)(log L)^q(.)

Fumi-Yuki Maeda, Yoshihiro Mizuta and Takao Ohno

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

Hiroshima University, Graduate School of Science, Department of Mathematics
Higashi-Hiroshima 739-8521, Japan; yomizuta 'at' hiroshima-u.ac.jp

Hiroshima National College of Maritime Technology, General Arts
Higashino Oosakikamijima Toyotagun 725-0231, Japan; ohno 'at' hiroshima-cmt.ac.jp

Abstract. Our aim in this paper is to deal with approximate identities in generalized Lebesgue spaces L^p(.)(log L)^q(.)(Rⁿ). As a related topic, we also study Young type inequalities for convolution with respect to norms in such spaces.

2000 Mathematics Subject Classification: Primary 46E30.

Key words: Lebesgue spaces of variable exponent, approximate identity, Young's inequality for convolution.

Reference to this article: F.-Y. Maeda, Y. Mizuta and T. Ohno: Approximate identities and Young type inequalities in variable Lebesgue-Orlicz spaces L^p(.)(log L)^q(.). Ann. Acad. Sci. Fenn. Math. 35 (2010), 405-420.

Full document as PDF file

doi:10.5186/aasfm.2010.3526

APPROXIMATE IDENTITIES AND YOUNG TYPE INEQUALITIES IN VARIABLE LEBESGUE-ORLICZ SPACES Lp(.)(log L)q(.)

Fumi-Yuki Maeda, Yoshihiro Mizuta and Takao Ohno

APPROXIMATE IDENTITIES AND YOUNG TYPE INEQUALITIES IN VARIABLE LEBESGUE-ORLICZ SPACES L^p(.)(log L)^q(.)