Abstract:
Characterizations of weighted integral Hardy inequalities identify the weights ensuring the boundedness of the Hardy operator on weighted Lebesgue spaces. This analysis has
been extended to the Riemann-Liouville operator and operators satisfying a weaker kernel condition, independently introduced by R. Oinarov [13] and by S. Bloom and R. Kerman [5]. While
Oinarov-type characterizations have been extended to the discrete case, Bloom-Kerman-type
characterizations, which differ, remain unexplored. This paper establishes these alternative characterizations for the discrete case and extends the results to a broader class of matrix operators,
including those satisfying weaker kernel conditions.
