Lower bounds of operators on weighted lp spaces and Lorentz sequence spaces

The problem considered is the determination of "lower bounds" of matrix operators on the spaces l(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.