Approximate identities and Young type inequalities in Musielak-Orlicz spaces

作者：Maeda Fumi Yuki^*; Mizuta Yoshihiro; Ohno Takao; Shimomura Tetsu

来源：Czechoslovak Mathematical Journal, 2013, 63(4): 933-948.

DOI：10.1007/s10587-013-0063-8

• approximate identity
• Musielak-Orlicz space
• Young type inequality

We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces.

• 出版日期2013-12