Two-Sided Estimates of the Norm for a Class of Matrix Operators
Aigerim Aisultankyzy Kalybay · Siberian Advances in Mathematics · 2022
For $$ 1<p,q<\infty $$ , we find 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 a class of matrix operators of the form $$(Af)_n=\sum \limits _{k=1}^{n}a_{n,k}f_k $$ , where $$n\ge 1 $$ .