Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 3

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

An interpolatory estimate for the UMD-valued directional Haar projection

100%
Lechner R.
Instytut Matematyczny Polskiej Akademii Nauk
EN
We prove an interpolatory estimate linking the directional Haar projection $P^{(ε)}$ to the Riesz transform in the context of Bochner-Lebesgue spaces $L^{p}(ℝⁿ;X)$, 1 < p < ∞, provided X is a UMD-space. If $ε_{i₀} = 1$, the result is the inequality $||P^{(ε)}u||_{L^{p}(ℝⁿ;X)} ≤ C||u||_{L^{p}(ℝⁿ;X)}^{1/𝓣} ||R_{i₀}u||_{L^{p}(ℝⁿ;X)}^{1 - 1/𝓣}$, (1) where the constant C depends only on n, p, the UMD-constant of X and the Rademacher type 𝓣 of $L^{p}(ℝⁿ;X)$. In order to obtain the interpolatory result (1) we analyze stripe operators $S_{λ}$, λ ≥ 0, which are used as basic building blocks to dominate the directional Haar projection. The main result on stripe operators is the estimate $||S_{λ}u||_{L^{p}(ℝⁿ;X)} ≤ C·2^{-λ/𝓒}||u||_{L^{p}(ℝⁿ;X)}$, (2) where the constant C depends only on n, p, the UMD-constant of X and the Rademacher cotype 𝓒 of $L^{p}(ℝⁿ;X)$. The proof of (2) relies on a uniform bound for the shift operators Tₘ, $0 ≤ m < 2^{λ}$, acting on the image of $S_{λ}$. Mainly based upon inequality (1), we prove a vector-valued result on sequential weak lower semicontinuity of integrals of the form u ↦ ∫ f(u)dx, where f: Xⁿ → ℝ⁺ is separately convex satisfying $f(x) ≤ C (1 + ||x||_{Xⁿ})^{p}$.
2
Content available remote

The One-Third-Trick and Shift Operators

96%
Lechner R.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2013
|
tom 61
|
nr 3
219-238
EN
We obtain a representation as martingale transform operators for the rearrangement and shift operators introduced by T. Figiel. The martingale transforms and the underlying sigma algebras are obtained explicitly by combinatorial means. The known norm estimates for those operators are a direct consequence of our representation.
3
Content available remote

Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type

61%
Lechner R., Passenbrunner M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2014
|
tom 62
|
nr 2
139-159
EN
In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.