Boundedness and compactness of a certain class of matrix operators with variable limits of summation

Necessary and sufficient conditions for the boundedness and compactness of the matrix operator of the form $(Af)_n=\sum_{k=\alpha(n)}^{\beta(n)}a_{n,k}f_k$, from $l_{p,v}$ to $l_{q,u}$ when $1<p\leqslant q<\infty$ are given.