On an inequality of Kolmogorov and Stein

Bang, Ha Huy; Le, Hoang Mai

doi:10.1017/s0004972700022103

Cited by 5 publications

(2 citation statements)

References 11 publications

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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

show abstract

“…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%