0000000000323138

AUTHOR

Lizaveta Ihnatsyeva

showing 4 related works from this author

Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space

2015

We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of R n and the relation between these spaces and traces of classical Sobolev spaces. This extends in a certain way the results of Shvartsman (20) to the case of lower dimensional subsets of the Euclidean space.

Pure mathematicsEight-dimensional spaceEuclidean spaceGeneral Mathematics010102 general mathematicsMathematical analysisSpace (mathematics)01 natural sciencesSobolev inequalitySobolev space0103 physical sciencesBesov spaceInterpolation space010307 mathematical physicsBirnbaum–Orlicz space0101 mathematicsMathematicsMathematische Nachrichten
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On improved fractional Sobolev–Poincaré inequalities

2016

We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.

Hölder's inequalityKantorovich inequalityPure mathematicsYoung's inequalityBernoulli's inequalityGeneral Mathematics010102 general mathematicsMathematical analysisMinkowski inequality01 natural sciences010101 applied mathematicsLog sum inequalityRearrangement inequality0101 mathematicsCauchy–Schwarz inequalityMathematicsArkiv för Matematik
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Fractional Hardy inequalities and visibility of the boundary

2013

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.

visibility of the boundaryPure mathematicsMathematics::Functional AnalysisInequalityfractional Hardy inequalitiesGeneral Mathematicsmedia_common.quotation_subject010102 general mathematicsVisibility (geometry)46E35 (26D15)Open setMathematics::Classical Analysis and ODEsOrder (ring theory)Boundary (topology)01 natural sciences010101 applied mathematicsMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematicsExposition (narrative)media_common
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Muckenhoupt $A_p$-properties of distance functions and applications to Hardy-Sobolev -type inequalities

2017

Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad (co)dimension of $E$, for the inclusion of $w$ in Muckenhoupt's $A_p$ classes of weights, $1\le p<\infty$. With the help of general $A_p$-weighted embedding results, we then prove (global) Hardy-Sobolev inequalities and also fractional versions of such inequalities in the setting of metric spaces.

Mathematics::Functional AnalysisMathematics - Analysis of PDEsAssouad dimensionMathematics - Classical Analysis and ODEsmetric spaceHardy-Sobolev inequalityClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Classical Analysis and ODEsMuckenhoupt weight42B25 (Primary) 31E05 35A23 (Secondary)Analysis of PDEs (math.AP)
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