On the Kolmogorov Inequality for <i>M</i> Φ -Norm

Bang, Ha Huy; Giao, Huynh Mong

doi:10.1080/0003681021000021033

Cited by 3 publications

(2 citation statements)

References 4 publications

(7 reference statements)

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“…Therefore the progress here is slower and at the moment there are many topical unsolved problems. We refer to the papers [3][4][5][6][21][22][23][24][25].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions

Kałamajska

Krbec

2010

Journal of Mathematical Analysis and Applications

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We consider a triple of N-functions (M, H, J ) that satisfy the -condition, μ = |x| α dx and suppose that an additive variant of interpolation inequality holds, R is an arbitrary set invariant with respect to external and internal dilations. We show that the above inequality implies its certain nonlinear variant involving the expressions R n H(|u|) μ(dx) and R n J (|∇ (2) u|) μ(dx). Various generalizations of this inequality to the more general class of N-functions, measures and to higher order derivatives are also discussed and the examples are presented.

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“…Therefore the progress here is slower and at the moment there are many topical unsolved problems. We refer to the papers [3][4][5][6][21][22][23][24][25].…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

Gagliardo–Nirenberg inequalities in regular Orlicz spaces involving nonlinear expressions

Kałamajska

Krbec

2010

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

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“…Although there is already a large body of literature about Sobolev inequalities in Orlicz spaces (see for example [8,15] and their references), to the best of our knowledge the interpolation inequalities between derivatives in Orlicz-Sobolev spaces are hardly discussed in the literature. We can refer the reader to recent papers by Bang [2], Bang and Giao [3], Bang and Le [4] and Bang and Thu [5], where the authors obtain Landau-Kolmogorov inequalities within a fixed Orlicz space.…”

Section: Introductionmentioning

confidence: 99%