Polynomial asymptotics and approximation of Sobolev functions

Piotr Hajłasz; Agnieszka Kałamajska

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Pointwise inequalities for Sobolev functions and some applications

Bogdan Bojarski, Piotr Hajłasz (1993)

Studia Mathematica

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We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by $C^{m}$ functions both in norm and capacity.

Linear extension operators for restrictions of function spaces to irregular open sets

V. Rychkov (2000)

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Sobolev type inequalities for p>0

Alberto Calderón, Ridgway Scott (1978)

Studia Mathematica

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Theory of Bessel potentials. II

Robert Adams, Nachman Aronszajn, K. T. Smith (1967)

Annales de l'institut Fourier

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Dans cette partie de la théorie des potentiels besseliens on considère les restrictions de potentiels de la classe $P^{a} (R^{n})$ aux domaines ouverts $D \subset R^{n}$ . On cherche à caractériser de manière intrinsèque la classe $P^{a} (D)$ ainsi obtenue. On attaque ce problème en définissant de manière directe (§ 2) une classe ${\overset{ˇ}{P}}^{a} (D) \subset P^{a} (D)$ qui, pour des domaines assez réguliers, est égale à $P^{a} (D)$ . L’égalité $P^{a} (D) = P^{a} (D)$ est équivalente à l’existence d’un opérateur-extension $E : {\overset{ˇ}{P}}^{a} (D) \to P^{a} (R^{n})$ , linéaire et continu, tel que $E u$ soit une extension...

Boundary values for Sobolev-spaces with weights. Density of $D (Ω) in W_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω) and in H_{p, γ_{0}, \dots, γ_{r}}^{s} (Ω)$ for $s$ > $0$ and $r = {[s - \frac{1}{p}]}^{-}$

Hans Triebel (1973)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Sobolev embeddings with variable exponent

David Edmunds, Jiří Rákosník (2000)

Studia Mathematica

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Best constants and asymptotics of Marcinkiewicz-Zygmund inequalities

Andreas Defant, Marius Junge (1997)

Studia Mathematica

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We determine the set of all triples 1 ≤ p,q,r ≤ ∞ for which the so-called Marcinkiewicz-Zygmund inequality is satisfied: There exists a constant c≥ 0 such that for each bounded linear operator $T : L_{q} (μ) \to L_{p} (ν)$ , each n ∈ ℕ and functions $f_{1}, . . ., f_{n} \in L_{q} (μ)$ , $(ʃ (\sum_{k = 1}^{n} | T f_{k} |^{r})^{p / r} {d ν)}^{1 / p} \leq c ∥ T ∥ (ʃ (\sum_{k = 1}^{n} | f_{k} |^{r} {)^{q / r} d μ)}^{1 / q}$ . This type of inequality includes as special cases well-known inequalities of Paley, Marcinkiewicz, Zygmund, Grothendieck, and Kwapień. If such a Marcinkiewicz-Zygmund inequality holds for a given triple (p,q,r), then we calculate the best constant c ≥ 0 (with the...

Addendum to the paper "On isomorphisms of anisotropic Sobolev spaces with "classical Banach spaces" and a Sobolev type embedding theorem"

A. Pełczyński, K. Senator (1986)

Studia Mathematica

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An approximation theorem in higher order Orlicz-Sobolev spaces and applications

A. Benkirane, J.-P. Gossez (1989)

Studia Mathematica

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Preduals of Sobolev-Campanato spaces

Konrad Gröger, Lutz Recke (2001)

Mathematica Bohemica

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We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.