Evgeniy Pustylnik

ON SHARP HIGHER ORDER SOBOLEV EMBEDDINGS

Let Ω be an open domain in ℝn, let k∈ℕ,

Sobolev inequalities: Symmetrization and self-improvement via truncation☆

p\le \frac{n}{k}

Optimal interpolation in spaces of Lorentz-Zygmund type

. Using a natural extension of the L(p, q) spaces and a new form of the Polya–Szego symmetrization principle, we extend the sharp version of the Sobolev embedding theorem:

Full length article: Convergence of non-periodic infinite products of orthogonal projections and nonexpansive operators in Hilbert space

W_0^{k, p} (\Omega)\subset L (\frac{np}{n -kp}, p) to the limiting value

New classes of rearrangement-invariant spaces appearing in extreme cases of weak interpolation

p =\frac{n}{k}

On strictly singular and strictly cosingular embeddings between Banach lattices of functions

. This result extends a recent result in [3] for the case k=1. More generally, if Y is a r.i. space satisfying some mild conditions, it is shown that

Some Extensions of Optimal Interpolation in Spaces of Lorentz–Zygmund Type

W_0^{k, Y} (\Omega)\subset Y_n (\infty, k) =\{f: t^{-k/n}(f^{\ast\ast} (t)-f^\ast (t))\in Y\}

Inexact Infinite Products of Nonexpansive Mappings

. Moreover Yn(∞,k) is not larger (and in many cases essentially smaller) than any r.i. space X(Ω) such that

Some Interpolation Results that are the Exclusive Property of Compact Operators

W_0^{k, Y} (\Omega)\subset X (\Omega)

Convergence to Compact Sets of Inexact Orbits of Nonexpansive Mappings in Banach and Metric Spaces

. This result extends, complements, simplifies and sharpens recent results in [10].