Recent developments in the theory of Lorentz spaces and weighted inequalities

Редукционные Теоремы Для Весовых Интегральных Неравенств На Конусе Монотонных Функций

“…(см., например, монографии [10], [15], [52], [56], [64], статьи [3], [4], [118], [16]- [18], [57]- [60], [70], [71], [80]- [86], [92]- [109], [113] и др. ).…”

Hardy's inequalities for monotone functions on partly ordered measure spaces

“…As mentioned above, the case of R + was first considered in [2]. B p weights are well understood and enjoy a very rich structure (see also [7,8,14] for an account of B p and normability properties of weighted Lorentz spaces). The discrete case N is a particular case of a tree, and can be found in [8].…”

“…B p weights are well understood and enjoy a very rich structure (see also [7,8,14] for an account of B p and normability properties of weighted Lorentz spaces). The discrete case N is a particular case of a tree, and can be found in [8]. Weights for a general tree were studied, without the monotonicity condition, in [1,9].…”

“…Weights for a general tree were studied, without the monotonicity condition, in [1,9]. It is easy to prove that a weight satisfying case 3 of corollary 2.3 must necessarily be in B p (N) (uniformly) on each geodesic (see [8]), but the converse is not true in general.…”

Some notes on embedding for anisotropic Sobolev spaces

“…If (X, µ) = (R + , w(t) dt), we replace L q,p (X) with L q,p (w). For 0 < p, q < ∞, or 0 < p ∞ and q = ∞, the weighted Lorentz space Λ p,q R n (w) = Λ p,q (w) is defined in [5,Ch. 2] by…”