Abstract:
In the article, we establish necessary and sufficient conditions for the validity of a discrete Hardy type inequality $$ \left(\sum\limits_{n=1}^{\infty}|(Af)_n|^q\right)^{\frac{1}{q}} \le C\left(\sum\limits_{k=1}^{\infty}|f_k|^p\right)^{\frac{1}{p}} $$ for one class of matrix operators $$(Af)_n=\sum\limits_{k=1}^{n}a_{n,k}f_k, n\ge 1,$$ for $1<p,q<\infty$.
Key words:Hardy type inequality, discrete operator, matrix operator, space of sequences.
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