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On integral operators with monotone kernels
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
2005 (russisk)Inngår i: Doklady Akademii Nauk, ISSN 0869-5652, Vol. 403, nr 1, s. 11-14Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The conditions are investigated, under which for all Lebesgue measurable functions f(x) greater than or equal 0 on a semi-axis R+:=(0, infinity ) with a constant C greater than or equal 0 independent of f, satisfied is inequality: {0 integral infinity [Kf(x)]qν(x)dx}1/q [less-than or equal to] C{0 integral infinity [f(x)]pu(x)dx}1/p (1) with measurable weighted functions u(x) greater than or equal 0 and ν(x) greater than or equal 0 and integral operator Kf(x):=0 integral infinity k(x,y)f(y)dy, where measurable in R+×R+ kernel k(x,y) greater than or equal 0 is monotone in one or two variables. Such operators can be exemplified with Laplace, Hilbert transforms etc. Further, the comparison theorems for (1)-type inequalities with the similar inequalities on a cone of non-growing functions for certain-type Volterra operators are proved.

sted, utgiver, år, opplag, sider
2005. Vol. 403, nr 1, s. 11-14
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Matematik
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URN: urn:nbn:se:ltu:diva-12188Scopus ID: 2-s2.0-27744535726Lokal ID: b4848660-b147-11db-bf9d-000ea68e967bOAI: oai:DiVA.org:ltu-12188DiVA, id: diva2:985138
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Validerad; 2005; 20070131 (ysko)

Tilgjengelig fra: 2016-09-29 Laget: 2016-09-29 Sist oppdatert: 2023-11-09bibliografisk kontrollert

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Persson, Lars-ErikStepanov, Vladimir D.Ushakova, Elena P.

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