Search results for "Null set"

showing 3 items of 13 documents

Pointwise characterizations of Hardy-Sobolev functions

2006

We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.

PointwiseMathematics::Functional Analysis42B30 (Primary) 26D15General Mathematics42B25 (Secondary)010102 general mathematicsMathematical analysisMathematics::Classical Analysis and ODEsMathematics::Analysis of PDEs01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceCombinatoricsNull setType conditionMathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: Mathematics46E35Locally integrable function0101 mathematics46E35; 42B30 (Primary) 26D15; 42B25 (Secondary)Mathematics
researchProduct

Absolutely continuous functions in Rn

2005

Abstract For each 0 α 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n , differentiable almost everywhere and satisfies the formula on change of variables.

Polish groupPure mathematicsChange of variablesα-regular intervalsContinuous functionApplied MathematicsMathematical analysisNull set or empty setQuasi-continuous functionAbsolute continuityWeak derivativeAbsolutely continuous functionsSobolev spaceHaar nullSobolev spacesAlmost everywhereDifferentiable functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
researchProduct

A decomposition theorem for σ-P-directionally porous sets in Fréchet spaces

2007

In this paper we study suitable notions of porosity and directional porosity in Fréchet spaces. Moreover we give a decomposition theorem for $\sigma$-$\mathcal{P}$-directionally porous sets.

Settore MAT/05 - Analisi Matematicalcsh:MathematicsDifferentiability of Lipschitz maps null setslcsh:QA1-939
researchProduct