Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function $f ∈ W^{k,p}(Ω)$ possesses an $L^{p}$ derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space $W^{k,p}(Ω)$. Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We prove that a function belonging to a fractional Sobolev space $L^{α,p}(ℝⁿ)$ may be approximated in capacity and norm by smooth functions belonging to $C^{m,λ}(ℝⁿ)$, 0 < m + λ < α. Our results generalize and extend those of [12], [4], [14], and [11].
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We construct a set B and homeomorphism f where f and $f^{-1}$ have property N such that the symmetric difference between the sets of density points and of f-density points of B is uncountable.
4
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.