The problem considered is the
determination of “lower bounds” of matrix operators on the spaces\ell_p(w)
or d(w,p). Under fairly general conditions, the
solution is the same for both spaces and is given by the infimum of a certain sequence. Specific cases
are considered, with the weighting sequence defined by w_n = 1/n^\alpha . The exact
solution is found for the Hilbert operator. For the averaging operator, two different upper bounds are
given, and for certain values of p and \alpha it is shown that
the smaller of these two bounds is the exact solution.