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Papers by Jesper Tidblom

arXiv: Analysis of PDEs, Feb 7, 2008

In this article we establish new improvements of the optimal Hardy inequality in the half space. ... more In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya type inequalities.

In this article we first establish a complete characterization of Hardy's inequalities in R n inv... more In this article we first establish a complete characterization of Hardy's inequalities in R n involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities. We then provide necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya inequalities with optimal Sobolev terms.

Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this articl... more Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. Hoffmann-Ostenhof and A. Laptev, which dealt with the special case p=2.Paper 2 : A Hardy inequality in the Half-space.Here we prove a Hardy-type inequality in the half-space which generalize an inequality originally proved by V. Maz'ya to the so-called L^p case. This inequality had previously been conjectured by the mentioned author. We will also improve the constant appearing in front of the reminder term in the original inequality (which is the first improved Hardy inequality appearing in the litterature).Paper 3 : Hardy type inequalities for Many-Particle systems.In this article we prove some results about the constants appearing in Har...

International Mathematical Series, 2009

In this article we first establish a complete characterization of Hardy's inequalities in R n inv... more In this article we first establish a complete characterization of Hardy's inequalities in R n involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities. We then provide necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya inequalities with optimal Sobolev terms.

Journal of the European Mathematical Society, 2009

We establish new improvements of the optimal Hardy inequality in the half-space. We first add all... more We establish new improvements of the optimal Hardy inequality in the half-space. We first add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya type inequalities.

Journal of the London Mathematical Society, 2007

In this paper we prove three different types of the socalled many-particle Hardy inequalities. On... more In this paper we prove three different types of the socalled many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimension d = 2. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a solenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.

arXiv: Analysis of PDEs, Feb 7, 2008

In this article we establish new improvements of the optimal Hardy inequality in the half space. ... more In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya type inequalities.

In this article we first establish a complete characterization of Hardy's inequalities in R n inv... more In this article we first establish a complete characterization of Hardy's inequalities in R n involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities. We then provide necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya inequalities with optimal Sobolev terms.

Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this articl... more Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. Hoffmann-Ostenhof and A. Laptev, which dealt with the special case p=2.Paper 2 : A Hardy inequality in the Half-space.Here we prove a Hardy-type inequality in the half-space which generalize an inequality originally proved by V. Maz'ya to the so-called L^p case. This inequality had previously been conjectured by the mentioned author. We will also improve the constant appearing in front of the reminder term in the original inequality (which is the first improved Hardy inequality appearing in the litterature).Paper 3 : Hardy type inequalities for Many-Particle systems.In this article we prove some results about the constants appearing in Har...

International Mathematical Series, 2009

In this article we first establish a complete characterization of Hardy's inequalities in R n inv... more In this article we first establish a complete characterization of Hardy's inequalities in R n involving distances to different codimension subspaces. In particular the corresponding potentials have strong interior singularities. We then provide necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya inequalities with optimal Sobolev terms.

Journal of the European Mathematical Society, 2009

We establish new improvements of the optimal Hardy inequality in the half-space. We first add all... more We establish new improvements of the optimal Hardy inequality in the half-space. We first add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy-Sobolev-Maz'ya type inequalities.

Journal of the London Mathematical Society, 2007

In this paper we prove three different types of the socalled many-particle Hardy inequalities. On... more In this paper we prove three different types of the socalled many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimension d = 2. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a solenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.

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