Search results for "Hardy"

Weighted Hardy inequalities beyond Lipschitz domains

2014

It is a well-known fact that in a Lipschitz domain \Omega\subset R^n a p-Hardy inequality, with weight d(x,\partial\Omega)^\beta, holds for all u\in C_0^\infty(\Omega) whenever \beta<p-1. We show that actually the same is true under the sole assumption that the boundary of the domain satisfies a uniform density condition with the exponent \lambda=n-1. Corresponding results also hold for smaller exponents, and, in fact, our methods work in general metric spaces satisfying standard structural assumptions.

Orlicz-Hardy inequalities

2004

We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. peerReviewed

Self-improvement of weighted pointwise inequalities on open sets

2020

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

Hardy-Orlicz Spaces of conformal densities

2014

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

Functions of One Variable

2019

A classical result of Fatou gives that every bounded holomorphic function on the disc has radial limits for almost every point in the torus, and the limit function belongs to the Hardy space H_\infty of the torus. This property is no longer true when we consider vector-valued functions. The Banach spaces X for which this property is satisfied are said to have the analytic Radon-Nikodym property (ARNP). Some important equivalent reformulations of ARNP are studied in this chapter. Among others, X has ARNP if and only if each X-valued H_p- function f on the disc has radial limits almost everywhere on the torus (and not only H_\infty-functions). Even more, in this case each such f has non-tange…

Hardy Spaces of Dirichlet Series

2019

Construction of O-minimal Structures from Quasianalytic Classes

2012

I present the method of constructing o-minimal structures based on local reduction of singularities for quasianalytic classes.

Quasiadditivity of Variational Capacity

2013

We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We characterize this property in terms of a Mazya type capacity condition, and also explore the close relation between quasiadditivity and Hardy's inequality.

Local maximal operators on fractional Sobolev spaces

2016

In this note we establish the boundedness properties of local maximal operators MG on the fractional Sobolev spaces Ws;p(G) whenever G is an open set in Rn, 0 < s < 1 and 1 < p < 1. As an application, we characterize the fractional (s;p)-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes. pq(G) whenever G is an open set in R n , 0 < s < 1 and 1 < p;q <1. Our main focus lies in the mapping properties of MG on a fractional Sobolev space W s;p (G) with 0 < s < 1 and 1 < p < 1, see Section 2 for the denition or (3) for a survey of this space. The intrinsically dened function space W s;p (G) on a given domain G coincides with the trace space F s …

PSMA6 (rs2277460, rs1048990), PSMC6 (rs2295826, rs2295827) and PSMA3 (rs2348071) genetic diversity in Latvians, Lithuanians and Taiwanese

2014

PSMA6 (rs2277460, rs1048990), PSMC6 (rs2295826, rs2295827) and PSMA3 (rs2348071) genetic diversity was investigated in 1438 unrelated subjects from Latvia, Lithuania and Taiwan. In general, polymorphism of each individual locus showed tendencies similar to determined previously in HapMap populations. Main differences concern Taiwanese and include presence of rs2277460 rare allele A not found before in Asians and absence of rs2295827 rare alleles homozygotes TT observed in all other human populations. Observed patterns of SNPs and haplotype diversity were compatible with expectation of neutral model of evolution. Linkage disequilibrium between the rs2295826 and rs2295827 was detected to be c…