Open this publication in new window or tab >>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. p. 84
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757
Keywords
Mathematics, Matematik
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
urn:nbn:se:ltu:diva-17410 (URN)3481b212-bf24-4cbe-a903-0a96fae3a186 (Local ID)978-91-7439-266-1 (ISBN)3481b212-bf24-4cbe-a903-0a96fae3a186 (Archive number)3481b212-bf24-4cbe-a903-0a96fae3a186 (OAI)
Presentation
2011-06-20, D2214/15, Luleå tekniska universitet, Luleå, 15:00
Opponent
2016-09-292016-09-292025-10-21Bibliographically approved