| 1. |
- Barreira, L, et al.
(författare)
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Higher-dimensional multifractal analysis
- 2002
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Ingår i: Journal des Mathématiques Pures et Appliquées. - 0021-7824. ; 81:1, s. 67-91
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Tidskriftsartikel (refereegranskat)abstract
- We establish a higher-dimensional version of multifractal analysis for several classes of hyperbolic dynamical systems. This means that we consider multifractal decompositions which are associated to multi-dimensional parameters. In particular, we obtain a conditional variational principle, which shows that the topological entropy of the level sets of pointwise dimensions, local entropies, and Lyapunov exponents can be simultaneously, approximated by the entropy of ergodic measures. A similar result holds for the Hausdorff dimension. This study allows us to exhibit new nontrivial phenomena absent in the one-dimensional multifractal analysis. In particular, while the domain of definition of a one-dimensional spectrum is always an interval, we show that for higher-dimensional spectra the domain may not be convex and may even have empty interior, while still containing an uncountable number of points. Furthermore, the interior of the domain of a higher-dimensional spectrum has in general more than one connected component.
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| 2. |
- Hedenmalm, Håkan, et al.
(författare)
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Hele-Shaw flow on hyperbolic surfaces
- 2002
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Ingår i: Journal des Mathématiques Pures et Appliquées. - 0021-7824 .- 1776-3371. ; 81:3, s. 187-222
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Tidskriftsartikel (refereegranskat)abstract
- Consider a complete simply connected hyperbolic surface. The classical Hadamard theorem asserts that at each point of the surface, the exponential mapping from the tangent plane to the surface defines a global diffeomorphism. This can be interpreted as a statement relating the metric flow on the tangent plane with that of the surface. We find an analogue of Hadamard's theorem with metric flow replaced by Hele-Shaw flow, which models the injection of (two-dimensional) fluid into the surface. The Hele-Shaw flow domains are characterized implicitly by a mean value property on harmonic functions.
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| 3. |
- Hedenmalm, Håkan
(författare)
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An off-diagonal estimate of Bergman kernels
- 2000
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Ingår i: Journal des Mathématiques Pures et Appliquées. - 0021-7824 .- 1776-3371. ; 79:2, s. 163-172
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Tidskriftsartikel (refereegranskat)abstract
- For weights on the unit disk that are logarithmically subharmonic and reproducing for the origin, an estimate from above and below is obtained for the Bergman kernel associated with the weight. In particular, that kernel is zero free, and bounded from above by twice the unweighted Bergman kernel.
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| 4. |
- Maz´ya, Vladimir G., et al.
(författare)
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On the brezis and mironescu conjecture concerning a Gagliardo-Nirenberg inequality for fractional Sobolev norms
- 2002
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Ingår i: Journal des Mathématiques Pures et Appliquées. - 0021-7824 .- 1776-3371. ; 81:9, s. 877-884
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Tidskriftsartikel (refereegranskat)abstract
- We prove the Gagliardo-Nirenberg type inequality where 0 < ? < 1, 0 < s < 1, 1 < p < 8, and ?u? Ws,p is the seminorm in the fractional Sobolev space Ws,p (Rn). The dependence of the constant factor in the right-hand side on each of the parameters s, ?, and p is precise in a sense. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.
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| 5. |
- Aleman, Alexandru, et al.
(författare)
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Composition of analytic paraproducts
- 2022
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Ingår i: Journal des Mathematiques Pures et Appliquees. - : Elsevier BV. - 0021-7824. ; 158, s. 293-319
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Tidskriftsartikel (refereegranskat)abstract
- For a fixed analytic function g on the unit disc D, we consider the analytic paraproducts induced by g, which are defined by Tgf(z)=∫0zf(ζ)g′(ζ)dζ, Sgf(z)=∫0zf′(ζ)g(ζ)dζ, and Mgf(z)=f(z)g(z). The boundedness of these operators on various spaces of analytic functions on D is well understood. The original motivation for this work is to understand the boundedness of compositions of two of these operators, for example Tg2,TgSg,MgTg, etc. Our methods yield a characterization of the boundedness of a large class of operators contained in the algebra generated by these analytic paraproducts acting on the classical weighted Bergman and Hardy spaces in terms of the symbol g. In some cases it turns out that this property is not affected by cancellation, while in others it requires stronger and more subtle restrictions on the oscillation of the symbol g than the case of a single paraproduct.
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| 6. |
- Björn, Anders, et al.
(författare)
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Extension and trace results for doubling metric measure spaces and their hyperbolic fillings
- 2022
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : Elsevier. - 0021-7824 .- 1776-3371. ; 159, s. 196-249
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study connections between Besov spaces of functions on a compactmetric space Z, equipped with a doubling measure, and the Newton–Sobolev spaceof functions on a uniform domain Xε. This uniform domain is obtained as auniformization of a (Gromov) hyperbolic filling of Z. To do so, we construct afamily of hyperbolic fillings in the style of Bonk–Kleiner [9] and Bourdon–Pajot [13]. Then for each parameter β > 0 we construct a lift μβ of the doubling measure νon Z to Xε, and show that μβ is doubling and supports a 1-Poincaré inequality.We then show that for each θ with 0 < θ < 1 and p ≥ 1 there is a choice of β = p(1 − θ)ε such that the Besov space is the trace space of the Newton–Sobolev space N1,p(Xε, μβ). Finally, we exploit the tools of potential theory on Xεto obtain fine properties of functions in , such as their quasicontinuity andquasieverywhere existence of Lq-Lebesgue points with q = sνp/(sν − pθ), where sν is a doubling dimension associated with the measure ν on Z. Applying this tocompact subsets of Euclidean spaces improves upon a result of Netrusov [43] in .
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| 7. |
- Björn, Anders, et al.
(författare)
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Local and semilocal Poincare inequalities on metric spaces
- 2018
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : ELSEVIER SCIENCE BV. - 0021-7824 .- 1776-3371. ; 119, s. 158-192
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Tidskriftsartikel (refereegranskat)abstract
- We consider several local versions of the doubling condition and Poincare inequalities on metric measure spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding within every ball. We then study various geometrical and analytical consequences of such local assumptions, such as local quasiconvexity, self-improvement of Poincare inequalities, existence of Lebesgue points, density of Lipschitz functions and quasicontinuity of Sobolev functions. It turns out that local versions of these properties hold under local assumptions, even though they are not always straightforward. We also conclude that many qualitative, as well as quantitative, properties of p-harmonic functions on metric spaces can be proved in various forms under such local assumptions, with the main exception being the Liouville theorem, which fails without global assumptions. (C) 2018 Elsevier Masson SAS. All rights reserved.
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| 8. |
- Cianchi, Andrea, et al.
(författare)
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Boundedness of solutions to the Schrodinger equation under Neumann boundary conditions
- 2012
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : Elsevier. - 0021-7824 .- 1776-3371. ; 98:6, s. 654-688
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Tidskriftsartikel (refereegranskat)abstract
- We deal with Neumann problems for Schrodinger type equations, with non-necessarily bounded potentials, in possibly irregular domains in R-n. Sharp balance conditions between the regularity of the domain and the integrability of the potential for any solution to be bounded are established. The regularity of the domain is described either through its isoperimetric function or its isocapacitary function. The integrability of the sole negative part of the potential plays a role, and is prescribed via its distribution function. The relevant conditions amount to the membership of the negative part of the potential to a Lorentz type space defined either in terms of the isoperimetric function, or of the isocapacitary function of the domain. (c) 2012 Elsevier Masson SAS. All rights reserved.
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| 9. |
- Cianchi, A., et al.
(författare)
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Neumann problems and isocapacitary inequalities
- 2008
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : Elsevier BV. - 0021-7824 .- 1776-3371. ; 89:1, s. 71-105
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Tidskriftsartikel (refereegranskat)abstract
- A priori bounds for solutions to (nonlinear) elliptic Neumann problems in open subsets O of Rn are established via inequalities relating the Lebesgue measure of subsets of O to their relative capacity. Both norm and capacitary estimates for solutions, and norm estimates for their gradients are derived which improve classical results even in the case of the Laplace equation. © 2007 Elsevier Masson SAS. All rights reserved.
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| 10. |
- Cianchi, Andrea, et al.
(författare)
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Optimal second-order regularity for the p-Laplace system
- 2019
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Ingår i: Journal des Mathématiques Pures et Appliquées. - : ELSEVIER. - 0021-7824 .- 1776-3371. ; 132, s. 41-78
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Tidskriftsartikel (refereegranskat)abstract
- Second-order estimates are established for solutions to the p-Laplace system with right-hand side in L-2. The nonlinear expression of the gradient under the divergence operator is shown to belong to W-1,W-2, and hence to enjoy the best possible degree of regularity. Moreover, its norm in 1471,2 is proved to be equivalent to the norm of the right-hand side in L-2. Our global results apply to solutions to both Dirichlet and Neumann problems, and entail minimal regularity of the boundary of the domain. In particular, our conclusions hold for arbitrary bounded convex domains. Local estimates for local solutions are provided as well. (C) 2019 Elsevier Masson SAS. All rights reserved.
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