Bilinear weighted Hardy inequality for nonincreasing functions

Abstract

We characterize the validity of the bilinear Hardy inequality for nonincreasing functions

Iterating Bilinear Hardy Inequalities

“…This operator is obviously a special case of T from (4.1). In [12], the iteration method was used to characterize boundedness H 2 :…”

“…(Notice that X 2 , Y are r.i., and thus the first two terms are indeed equal.) Since we know that in this case • Y • Γ + • K , the problem is reduced to finding the optimal constants for certain embeddings Λ → Γ and Λ → K. Characterizations of Λ → Γ are well known (see, for example, [4,6]); the problem of Λ → K was studied in [12].…”

“…Especially in the 'easy case' p 1 , p 2 q, the proof becomes extremely simple. Let us note that the same idea was also used in [12] to characterize the bilinear Hardy inequality for decreasing functions.…”

Discrete bilinear Hardy inequalities

“…где константа C не зависит от a и b и полагается наименьшей из возможных. Билинейные весовые неравенства на конусах неотрицательных функций изучались в работах [1][2][3][4][5][6][7][8].…”