BEST POSSIBLE RESULTS IN A CLASS OF INEQUALITIES .2.

[摘要] We give a sufficient condition on a lower triangular infinite matrix A with nonnegative entries, and a positive sequence b = (b(n)), for an inequality of the form \\A(b\x\)\\(p) less than or equal to K\\x\\(p), x is an element of l(p), to be best possible, in the sense that there is no positive sequence d = (d(n)) such that (d(n)b(n)(-1)) is a monotone unbounded sequence, and an inequality of the form above holds with b replaced by d. This condition permits easy proofs of ''best possible'' theorems that generalize a previous result concerning Hardy's inequality. (C) 1994 Academic Press, Inc.

[发布日期] 1994-12-15