Search results for "Absolute"
showing 10 items of 518 documents
Relations between natural and observable measures
2005
We give a complete description of relations between observable and natural measures in connection with invariance, ergodicity and absolute continuity.
Absolutely continuous functions and differentiability in Rn
2002
Abstract We relativize the notion of absolute continuity of functions in R n , due to Rado, Reichelderfer and Malý, to subsets of R n and use it to characterize functions (possibly vector valued) differentiable almost everywhere.
Projective Crystalline Representations of \'Etale Fundamental Groups and Twisted Periodic Higgs-de Rham Flow
2017
This paper contains three new results. {\bf 1}.We introduce new notions of projective crystalline representations and twisted periodic Higgs-de Rham flows. These new notions generalize crystalline representations of \'etale fundamental groups introduced in [7,10] and periodic Higgs-de Rham flows introduced in [19]. We establish an equivalence between the categories of projective crystalline representations and twisted periodic Higgs-de Rham flows via the category of twisted Fontaine-Faltings module which is also introduced in this paper. {\bf 2.}We study the base change of these objects over very ramified valuation rings and show that a stable periodic Higgs bundle gives rise to a geometric…
Integration of both the derivatives with respect to P-paths and approximative derivatives
2009
In the present paper, in terms of generalized absolute continuity, we present a descriptive characteristic of the primitive with respect to a system of P-paths and study the relationship between the Denjoy-Khinchin integral and the Henstock H P-integral. © 2009 Pleiades Publishing, Ltd.
On the problem of regularity in the Sobolev space Wloc1,n
2009
Abstract We prove that a variant of the Hencl's notion of A C λ n -mapping (see [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189]), in which λ is not a constant, produces a new solution to the problem of regularity in the Sobolev space W loc 1 , n .
A new full descriptive characterization of Denjoy-Perron integral
1995
It is proved that the absolute continuity of the variational measure generated by an additive interval function \(F\) implies the differentiability almost everywhere of the function \(F\) and gives a full descriptive characterization of the Denjoy-Perron integral.
On $L^p$ resolvent estimates for Laplace-Beltrami operators on compact manifolds
2011
Abstract. In this article we prove Lp estimates for resolvents of Laplace–Beltrami operators on compact Riemannian manifolds, generalizing results of Kenig, Ruiz and Sogge (1987) in the Euclidean case and Shen (2001) for the torus. We follow Sogge (1988) and construct Hadamard's parametrix, then use classical boundedness results on integral operators with oscillatory kernels related to the Carleson and Sjölin condition. Our initial motivation was to obtain Lp Carleman estimates with limiting Carleman weights generalizing those of Jerison and Kenig (1985); we illustrate the pertinence of Lp resolvent estimates by showing the relation with Carleman estimates. Such estimates are useful in the …
On the inverse absolute continuity of quasiconformal mappings on hypersurfaces
2018
We construct quasiconformal mappings $f\colon \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ for which there is a Borel set $E \subset \mathbb{R}^2 \times \{0\}$ of positive Lebesgue $2$-measure whose image $f(E)$ has Hausdorff $2$-measure zero. This gives a solution to the open problem of inverse absolute continuity of quasiconformal mappings on hypersurfaces, attributed to Gehring. By implication, our result also answers questions of V\"ais\"al\"a and Astala--Bonk--Heinonen.
Some new results on integration for multifunction
2018
It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.
Absolutely continuous variational measures of Mawhin's type
2011
Abstract In this paper we study absolutely continuous and σ-finite variational measures corresponding to Mawhin, F- and BV -integrals. We obtain characterization of these σ-finite variational measures similar to those obtained in the case of standard variational measures. We also give a new proof of the Radon-Nikodým theorem for these measures.