ALTERNATIVE CRITERIA FOR BOUNDEDNESS OF ONE CLASS OF MATRIX OPERATORS IN WEIGHTED SPACES OF SEQUENCES

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.