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Some new Hardy-type inequalities on the cone of monotone functions
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- Shambilova, Guldarya, 1977- (author)
- Luleå tekniska universitet,Matematiska vetenskaper
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- Wall, Peter, Professor (thesis advisor)
- Luleå tekniska universitet,Matematiska vetenskaper
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- Persson, Lars-Erik, Professor (thesis advisor)
- Luleå tekniska universitet,Matematiska vetenskaper
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- (creator_code:org_t)
- ISBN 9789177901020
- Luleå : Luleå University of Technology, 2018
- English.
- Series: Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, 1402-1544
- Doctoral thesis (other academic/artistic)
Abstract
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- This PhD thesis is devoted to the study weighted Hardy-type inequalitieswith quasilinear integral operators on the cone of monotone functions. Thethesis consists of six papers (papers A - F) and an introduction, which givesa brief review of the theory of Hardy-type inequalities and also serves to putthese papers into a more general frame.In papers A, D and E we characterize some weighted Hardy-type inequal-ities on the cone of non-increasing functions. This problem is related to theboundedness of the Hardy-Littlewood maximal operator in weighted LorentzΓ - spaces. In papers D and E the case with integral operators defined byso called Oinarov’s kernels are treated. In all cases necessary and sufficientconditions are derived.In paper B we solve the similar problem for the cone of quasi-concavefunctions (i.e. when the function f satisfy two monotonicity conditions,namely that f (t) is non-decreasing and f(t)t is non-increasing). Such functions are of great importance for interpolation theory, approximation theory and related areas in functional analysis. Also here complete characterizations are given in all cases.Paper C is devoted to characterizing weighted Hardy-type inequalities with supremum operators on the cone of monotone functions. In particular, the study of the case with non-decreasing functions was initiated in this paper.In paper F we focus only on the much less studied problem, namely to characterize Hardy-type inequalities on the cone of non-decreasing functions. A new reduction method is used in a crucial way. Some complete charac-terizations for all studied cases are discussed and proved. The investigations initiated in paper C are here developed to a more general theory, which cov-ers all studied operators. The obtained results are used to derive some new bilinear Hardy-type inequalities.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Mathematics
- Matematik
Publication and Content Type
- vet (subject category)
- dok (subject category)
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