Weighted norm inequalities for a nonlinear transform

Nhan, Nguyen Du Vi; Duc, Dinh Thanh; Tuan, Vu Kim

doi:10.1016/j.camwa.2010.12.031

Cited by 12 publications

(6 citation statements)

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“…In this section, we combine the methods of [4] with the ideas of Yamada [12] to yield a norm inequality for derivatives of products of compositions of functions which extends and generalizes some recent results of Nhan, Duc and 229 weighted norm inequalities for derivatives Tuan [8], Nhan and Duc [4], Yamada [12], Saitoh [11,10], and some earlier results on Opial-type inequalities [1].…”

Section: Norm Inequalities For Products Of Composition Of Functionsmentioning

confidence: 92%

“…Independently, some results of Saitoh in [11] were also generalized by the authors [8], in which we presented some weighted norm inequalities for a nonlinear transform in di¤erent normed spaces.…”

mentioning

confidence: 87%

“…j f 0 ðxÞj 2 dx: ð1:1Þ Opial-type inequalities involving integrals of functions and their derivatives are essential and in fact indispensable in the theory of di¤erential equations. In [12], Yamada considered an elementary integral inequality which extended a norm inequality of Saitoh [11] and yielded some well-known Opial-type inequalities (see [1]).Independently, some results of Saitoh in [11] were also generalized by the authors [8], in which we presented some weighted norm inequalities for a nonlinear transform in di¤erent normed spaces.Recently, the first two authors [4] considered some norm inequalities for derivatives of products of functions which generalize Saitoh's result [10] and provide an e¤ective tool to estimate Fourier sine and Fourier cosine transforms.In this paper, we will obtain weighted norm inequalities for derivatives of products of composition of functions which generalize some results from ([4], [8]), 228 2010 Mathematics Subject Classification. 26D10; 26A46; 46E35; 44A35.…”

mentioning

confidence: 95%

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Weighted norm inequalities for derivatives and their applications

Nhan¹,

Thanh²,

Kim³

2013

Kodai Math. J.

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In this paper we establish several weighted norm inequalities for derivatives of products of composition and Laplace convolution of functions. Some generalizations including Yamada's and Opial-type inequalities are discussed. As applications we give L p -weighted estimates for solutions of some integral equations. j f 0 ðxÞj 2 dx: ð1:1Þ Opial-type inequalities involving integrals of functions and their derivatives are essential and in fact indispensable in the theory of di¤erential equations. In [12], Yamada considered an elementary integral inequality which extended a norm inequality of Saitoh [11] and yielded some well-known Opial-type inequalities (see [1]).Independently, some results of Saitoh in [11] were also generalized by the authors [8], in which we presented some weighted norm inequalities for a nonlinear transform in di¤erent normed spaces.Recently, the first two authors [4] considered some norm inequalities for derivatives of products of functions which generalize Saitoh's result [10] and provide an e¤ective tool to estimate Fourier sine and Fourier cosine transforms.In this paper, we will obtain weighted norm inequalities for derivatives of products of composition of functions which generalize some results from ([4], [8]), 228 2010 Mathematics Subject Classification. 26D10; 26A46; 46E35; 44A35.

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Section: Norm Inequalities For Products Of Composition Of Functionsmentioning

confidence: 92%

mentioning

confidence: 87%

mentioning

confidence: 95%

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Weighted norm inequalities for derivatives and their applications

Nhan¹,

Thanh²,

Kim³

2013

Kodai Math. J.

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“…Most recent theoretical results related to inequalities include: generalized vector variational-type inequalities [9], Jensen type inequalities [1], Hölder's inequality [17] or weighted norm inequalities [13]. The reader can find in the literature many applications of these inequalities.…”

Section: Introductionmentioning

confidence: 99%

Several refinements and counterparts of Radon's inequality

Raţiu¹,

Minculete²

2015

Math. Bohem.

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We establish that the inequality of Radon is a particular case of Jensen's inequality. Starting from several refinements and counterparts of Jensen's inequality by Dragomir and Ionescu, we obtain a counterpart of Radon's inequality. In this way, using a result of Simić we find another counterpart of Radon's inequality. We obtain several applications using Mortici's inequality to improve Hölder's inequality and Liapunov's inequality. To determine the best bounds for some inequalities, we used Matlab program for different cases.

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“…From (1.2), various norm inequalities (see [7,14,15,16,17,18,19]) in reproducing kernel Hilbert spaces were obtained, which were generalized and reproved using various technics and were expanded for various directions with applications to inverse problems and partial differential equations (see [1,4,5,6,8,10,11,9,12,13]).…”

Section: Introductionmentioning

confidence: 99%