A generalization of Hardy's inequality to infinite tensors.

In this paper, we extend Hardy's inequality to infinite tensors. To do so, we introduce Cesàro tensors ℭ , and consider them as tensor maps from sequence spaces into tensor spaces. In fact, we prove inequalities of the form ∥ ℭ ⁢ x k ∥ t , 1 ≤ U ⁢ ∥ x ∥ l p k ( k = 1 , 2 ), where x is a sequence, ℭ ⁢ x k is a tensor, and ∥ ⋅ ∥ t , 1 , ∥ ⋅ ∥ l p are the tensor and sequence norms, respectively. The constant U is independent of x, and we seek the smallest possible value of U. [ABSTRACT FROM AUTHOR]