This paper surveys results related to the reduction of integral inequalities involving positive
operators in weighted Lebesgue spaces on the real semi-axis and valid on the cone of …

Редукционные теоремы для весовых интегральных неравенств на конусе м Page 1 2013 г.
июль — август т. 68, вып. 4(412) УСПЕХИ МАТЕМАТИЧЕСКИХ НАУК УДК 517.51 …

In this paper a reduction and equivalence theorems for the boundedness of the composition
of a quasilinear operator $ T $ with the Hardy and Copson operators in weighted Lebesgue …

We characterize the validity of the Hardy‐type inequality∥∥∫ s∞ h (z) dz∥ p, u,(0, t)∥ q,
w,(0,∞)≤ c∥ h∥ θ, v (0,∞), where 0< p<∞, 0< q≤∞, 1< θ≤∞, u, w, and v are weight …

An iteration technique for characterizing boundedness of certain types of multilinear
operators is presented, reducing the problem to a corresponding linear-operator case. The …

We study a three-weight inequality for the superposition of the Hardy operator and the
Copson operator, namely (∫ ab (∫ tb (∫ asf (τ) pv (τ) d τ) qpu (s) ds) rqw (t) dt) 1 r≤ C∫ …

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of
monotone functions in the Lp− Lq setting for 0< q<∞, 1≤ p<∞. The case 0< p< 1 is also …

In this paper we characterize the validity of the Hardy-type inequality∥∥∫ s∞ h (z) dz∥ p,
u,(0, t)∥ q, w,(0,∞)≤ c∥ h∥ 1, v,(0,∞), where 0< p<∞, 0< q≤+∞, u, w and v are weight …

We characterize the validity of the bilinear Hardy inequality for nonincreasing functions
‖f^**g^**‖_L^q(w)≤C‖f‖_Λ^p_1(v_1)‖g‖_Λ^p_2(v_2), in terms of the weights v_1 …

In this paper we calculate the norm of the generalized maximal operator $ M_
{\phi,\Lambda^{\alpha}(b)} $, defined with $0<\alpha<\infty $ and functions $ b,\,\phi:(0,\infty) …