Temat: $l^p$-spaces - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On constructions of isometric copies of $L^p (0, 1)$ spaces $(0 \lt p \leq 2)$ by stochastic $p$-stable processes
Autorzy:: Grala-Michalak, Jolanta
Michalak, Artur
Powiązania:: https://bibliotekanauki.pl/articles/746599.pdf
Data publikacji:: 2008
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: $L^p$-spaces
Opis:: Let $S^p = \{S_t^p : t = \frac{k}{2^n},\ 0 \leq k \leq 2^n,\ n \in\mathbb{N}\}$ be a stochastic process on a probability space $(\Omega, \Sigma, P)$ with independent and time homogeneous increments such that $S_t^p - S_u^p$ is identically distributed as $(t- u)^{1/p} Z_p$ for each $0 \leq u \lt t \leq 1$ where $Z_p$ is a given symmetric $p$-stable distribution. We show that the closed linear hull of $S^p$ forms an isometric copy of the real Lebesgue space $L^p (0, 1)$ in any quasi-Banach space $X$ consisting of $P$-a.e. equivalence classes of $\Sigma$-measurable real functions on $\Omega$ equipped with a rearrangement invariant quasi-norm which contains $S^p$ as a subset. It is possible to construct processes $S^p$ for $0 \lt p \leq 2$ on $[0, 1]$ with the Lebesgue measure. We show also a complex version of the result.
Źródło:: Commentationes Mathematicae; 2008, 48, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: On constructions of isometric embeddings of nonseparable $L^p$ spaces, $0 \lt p \leq 2$
Autorzy:: Grala-Michalak, Jolanta
Michalak, Artur
Powiązania:: https://bibliotekanauki.pl/articles/745759.pdf
Data publikacji:: 2008
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: $L^p$-spaces
Opis:: Let $J$ be an infinite set. Let $X$ be a real or complex $\sigma$-order continuous rearrangement invariant quasi-Banach function space over $(\{0, 1\}^J,\ \mathcal{B}^J,\ \lambda_J)$, the product of $J$ copies of the measure space $(\{0, 1\},\ 2^{0,1},\ \frac{1}{2} \delta_0 + \frac{1}{2}\delta_1)$. We show that if $0 \lt p \lt 2$ and $X$ contains a function $f$ with the decreasing rearrangement $f^∗$ such that $f^∗(t) \gt t^{-\frac{1}{p}}$ for every $t\in (0, 1)$, then it contains an isometric copy of the Lebesgue space $L^p (\lambda_J)$. Moreover, if $X$ contains a function $f$ such that $f^∗(t) \gt \sqrt{|\text{ln}(t)|}$ for every $t\in (0, 1)$, then it contains an isometric copy of the Lebesgue space $L^2(\lambda_J)$.
Źródło:: Commentationes Mathematicae; 2008, 48, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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