منابع مشابه
Carleman type inequalities and Hardy type inequalities for monotone functions
This Ph.D. thesis deals with various generalizations of the inequalities by Carleman, Hardy and Pólya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman’s inequality, which may be regarded as a discrete version of Pólya-Knopp’s inequality and also as a natural limiting inequality of the discre...
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Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...
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We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...
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In this paper, we will prove some new dynamic inequalities on a time scale T. These inequalities, as special cases, when T= R contain some integral inequalities and when T= N contain the discrete inequalities due to Leindler. The main results will be proved by using the Hölder inequality and a simple consequence of Keller’s chain rule on time scales. From our results, as applications, we will d...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2004
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700034778