Related papers: Hardy inequalities and Assouad dimensions
In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…
We consider closed biharmonic hypersurfaces in the Euclidean sphere and prove a rigidity result under a suitable condition on the scalar curvature. Moreover, we establish an integral formula involving the position vector for biharmonic…
We prove global higher integrability for functionals of double-phase type under a uniform local capacity density condition on the complement of the considered domain $\Omega \subset \mathbb{R}^n$. In this context, we investigate a new…
The aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compact approximation properties (shortly, BCAP and DCAP) of such…
We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C^\infty domains and Lipschitz domains.
We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, which converges to the critical Hardy inequality. Sobolev type…
We prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an inequality for functions defined on the…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…
This paper studies the weighted Hardy inequalities on the discrete intervals with four different kinds of boundary conditions. The main result is the uniform expression of the basic estimate of the optimal constant with the corresponding…
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales. We show that some such results remain valid for metric spaces with non-unique…
The paper is devoted to weighted $L^p$-Hardy inequalities with best constants on Finsler metric measure manifolds. There are two major ingredients. The first, which is the main part of this paper, is the Hardy inequalities concerned with…
We study the Assouad and quasi-Assoaud dimensions of dominated rectangular self-affine sets in the plane. In contrast to previous work on the dimension theory of self-affine sets, we assume that the sets satisfy certain separation…
We find a necessary and sufficient condition for a doubling metric space to carry a (1,p)-Poincare inequality. The condition involves discretizations of the metric space and Poincare inequalities on graphs.
We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group…
We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.
We introduce moduli spaces of quasi-admissible hyperelliptic covers with at worst A and D singularities. The stability conditions for these moduli spaces depend on two parameters describing allowable singularities. By varying these…
We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.
In this work we improve the sharp Hardy inequality in the case $p>n$ by adding an optimal weighted Hoelder semi-norm. To achieve this we first obtain a local improvement. We also obtain a refinement of both the Sobolev inequality for $p>n$…
Inspired by the many applications of mutually unbiased Hadamard matrices, we study mutually unbiased weighing matrices. These matrices are studied for small orders and weights in both the real and complex setting. Our results make use of…