Geodesic
Approximate identities and Young type inequalities in Musielak-Orlicz spaces
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 933-948
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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.
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.
DOI : 10.1007/s10587-013-0063-8
Classification : 46E30
Keywords: approximate identity; Musielak-Orlicz space; Young type inequality 
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Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu. Approximate identities and Young type inequalities in Musielak-Orlicz spaces. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 4, pp. 933-948. doi: 10.1007/s10587-013-0063-8

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