Lebesgue-Stieltjes integral and young's inequality

Autor:	Milan Merkle, Monica Moulin Ribeiro Merkle, Dan Ştefan Marinescu, Marian Stroe, Mihai Monea
Rok vydání:	2014
Předmět:	Discrete mathematics Young's inequality Change of variables Applied Mathematics Riemann–Stieltjes integral Lebesgue integration Measure (mathematics) Combinatorics symbols.namesake Number theory symbols Discrete Mathematics and Combinatorics Integration by parts Real line Analysis Mathematics
Zdroj:	Applicable Analysis and Discrete Mathematics. 8:60-72
ISSN:	2406-100X 1452-8630
DOI:	10.2298/aadm131211024m
Popis:	For non-decreasing real functions f and g; we consider the functional T(f,g; I,J) = ?I f(x) dg(x) + ?J g(x) df(x); where I and J are intervals with J ? I. In particular case with I = [a, t]; J = [a, s], a < s ? t and g(x) = x; this reduces to the expression in classical Young's inequality. We survey some properties of Lebesgue-Stieltjes integrals and present a simple proof for change of variables. Further, we formulate a version of Young's inequality with respect to arbitrary positive measure on real line and discuss applications in probability and number theory.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8c2843cafcc672cd3719e087fe529e04 https://doi.org/10.2298/aadm131211024m Zobrazit plný text záznamu Plný text ve formátu PDF