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Sharp estimates for the identity minus Hardy operator on the cone of decreasing functions
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Global Sun Engineering AB, Luleå, Sweden.
2008 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 7, p. 2505-2513Article in journal (Refereed) Published
##### Abstract [en]

It is shown that if we restrict the identity minus Hardy operator on the cone of nonnegative decreasing functions f in L-p, then we have the sharp estimate parallel to(I - H)f parallel to(Lp) <= 1/(p - 1)(1/p) parallel to f parallel to(Lp) for p = 2, 3, 4, .... In other words,parallel to f** - f*parallel to(Lp) <= 1/(p - 1)(1/p) parallel to f parallel to(Lp) for each f is an element of L-p and each integer p >= 2.It is also shown, via a connection between the operator I - H and Laguerre functions, thatparallel to(1 - alpha)I + Phi(I - H)parallel to(L2 -> L2) = parallel to I - alpha H parallel to(L2 -> L2) = 1 for all a is an element of [ 0, 1].

##### Place, publisher, year, edition, pages
2008. Vol. 136, no 7, p. 2505-2513
##### National Category
Mathematical Analysis
Mathematics
##### Identifiers
ISI: 000254675200029Scopus ID: 2-s2.0-77950803201Local ID: 776ed380-6c44-11dc-89fb-000ea68e967bOAI: oai:DiVA.org:ltu-8914DiVA, id: diva2:981852
##### Note

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Kruglyak, Natan

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