Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity

Autor:	Łochowski, R. M.
Rok vydání:	2016
Předmět:	Mathematics - Functional Analysis 46B99 46G10
Zdroj:	Journal of Inequalities and Applications 2018,2018:20
Druh dokumentu:	Working Paper
DOI:	10.1186/s13660-018-1611-4
Popis:	We prove an inequality of the Lo\'{e}ve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals. Also, for any $p\ge1$ we introduce the space of regulated signals $f:[a,b] \rightarrow W$ ($a0$ by signals whose total variation is of order $\delta^{1-p}$ as $\delta\rightarrow 0+$ and prove that they satisfy the assumptions of the theorem. Finally, we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by such signals. Comment: arXiv admin note: text overlap with arXiv:1409.3757
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1602.02269 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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