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- Abylayeva, AkbotaLuleå tekniska universitet,Institutionen för teknikvetenskap och matematik (författare)
Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces
- BokEngelska2016
Förlag, utgivningsår, omfång ...
- 2016
- electronicrdacarrier
Nummerbeteckningar
- LIBRIS-ID:oai:DiVA.org:ltu-59667
- ISBN:9789175837093
- ISBN:9789175837109
- https://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-59667URI
Kompletterande språkuppgifter
- Språk:engelska
- Sammanfattning på:engelska
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Klassifikation
Serie
- Doctoral thesis / Luleå University of Technology 1 jan 1997 → …,1402-1544
Anmärkningar
- This PhD thesis is devoted to investigate weighted differential Hardy inequalities and Hardy-type inequalities with the kernel when the kernel has an integrable singularity, and also the additivity of the estimate of a Hardy type operator with a kernel.The thesis consists of seven papers (Papers 1, 2, 3, 4, 5, 6, 7) and an introduction where a review on the subject of the thesis is given. In Paper 1 weighted differential Hardy type inequalities are investigated on the set of compactly supported smooth functions, where necessary and sufficient conditions on the weight functions are established for which this inequality and two-sided estimates for the best constant hold. In Papers 2, 3, 4 a more general class of -order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < < 1. In Papers 2 and 3 the boundedness and compactness of two classes of such operators are investigated namely of Weyl and Riemann-Liouville type, respectively, in weighted Lebesgue spaces for 1 < p ≤ q < 1 and 0 < q < p < ∞. As applications some new results for the fractional integration operators of Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard are given and discussed.In Paper 4 the Riemann-Liouville type operator with variable upper limit is considered. The main results are proved by using a localization method equipped with the upper limit function and the kernel of the operator. In Papers 5 and 6 the Hardy operator with kernel is considered, where the kernel has a logarithmic singularity. The criteria of the boundedness and compactness of the operator in weighted Lebesgue spaces are given for 1 < p ≤ q < ∞ and 0 < q < p < ∞, respectively. In Paper 7 we investigated the weighted additive estimates for integral operators K+ and K¯ defined byK+ ƒ(x) := ∫ k(x,s) ƒ(s)ds, K¯ ƒ(x) := ∫ k(x,s)ƒ(s)ds.It is assumed that the kernel k of the operators K+and K- belongs to the general Oinarov class. We derived the criteria for the validity of these addittive estimates when 1 ≤ p≤ q < ∞
Ämnesord och genrebeteckningar
- NATURVETENSKAP Matematik Matematisk analys hsv//swe
- NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
- Mathematics
- Matematik
Biuppslag (personer, institutioner, konferenser, titlar ...)
- Wall, PeterLuleå tekniska universitet,Institutionen för teknikvetenskap och matematik (preses)
- Persson, Lars-ErikLuleå tekniska universitet,Institutionen för teknikvetenskap och matematik (preses)
- Oinarov, Ryskul (preses)
- Luleå tekniska universitetInstitutionen för teknikvetenskap och matematik (creator_code:org_t)
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