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Keywords:
discrete Hardy operator; dual operator; weight function; weighted Musielak-Orlicz sequence space; embedding theorem; boundedness
Summary:
We establish a necessary and sufficient condition on weight functions for the boundedness of the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces. In particular, we get similar results for the dual operator of the discrete Hardy operator. We give sufficient pointwise conditions on generalized $\Phi $-functions that guarantee continuous embeddings between weighted Musielak-Orlicz sequence spaces. The results are illustrated by a number of corollaries.
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