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Hardy-type inequalities on cones of monotone functions
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This Licentiate thesis deals with Hardy-type inequalities restricted to cones of monotone functions. The thesis consists of two papers (paper A and paper B) and an introduction which gives an overview to this specific field of functional analysis and also serves to put the papers into a more general frame.We deal with positive $\sigma $-finite Borel measures on ${\mathbbR}_{+}:=[0,\infty)$ and the class $\mathfrak{M}\downarrow $($\mathfrak{M}\uparrow $) consisting of all non-increasing(non-decreasing) Borel functions $f\colon{\mathbbR}_{+}\rightarrow[0,+\infty ]$.In paper A some two-sided inequalities for Hardy operators on thecones of monotone functions are proved. The idea to study suchequivalences follows from the Hardy inequality$$\left( \int_{[0,\infty)}f^pd\lambda\right)^{\frac{1}{p}}\le \left(\int_{[0,\infty)} \left( \frac{1}{\Lambda(x)} \int_{[0,x]}f(t)d\lambda(t)\right)^p d\lambda(x)\right)^{\frac{1}{p}}$$$$\leq \frac{p}{p-1}\left(\int_{[0,\infty)}f^pd\lambda\right)^{\frac{1}{p}},$$which holds for any $f\in \mathfrak{M}\downarrow$ and $1

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2011. , 84 p.
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
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URN: urn:nbn:se:ltu:diva-17410Local ID: 3481b212-bf24-4cbe-a903-0a96fae3a186ISBN: 978-91-7439-266-1OAI: diva2:990415
Godkänd; 2011; 20110510 (olgpop); LICENTIATSEMINARIUM Ämnesområde: Matematik/Mathematics Examinator: Professor Lars-Erik Persson, Institutionen för teknikvetenskap och matematik, Luleå tekniska universitet Diskutant: Docent Lyudmila Turowska, Institutionen för matematiska vetenskaper, Chalmers tekniska högskola Tid: Måndag den 20 juni 2011 kl 15.00 Plats: D2214/15, Luleå tekniska universitetAvailable from: 2016-09-29 Created: 2016-09-29Bibliographically approved

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