Related papers: Semigroup inequalities, stochastic domination, Har…

We develop a robust structure theory for multiple ergodic averages of commuting transformations along Hardy sequences of polynomial growth. We then apply it to derive a number of novel results on joint ergodicity, recurrence and…

We present an introduction to periodic and stochastic homogenization of ellip- tic partial differential equations. The first part is concerned with the qualitative theory, which we present for equations with periodic and random coefficients…

In this note, it is shown that the results claimed in the paper [1]---as well as the examples presented there---are, unfortunately, incorrect.

New Hardy type inequality with double singular kernel and with additional logarithmic term in a ball $B\subset \mathbb{R}^n$ is proved. As an application an estimate from below of the first eigenvalue for Dirichlet problem of p-Laplacian in…

Key Words: Hardy inequalities, Sobolev inequalities, Morrey inequality, distance function, mean curvature, best constants, semi-concavity, sets with positive reach, mean convex sets, Cheeger constant, modulus of continuity

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hardy inequality in a half-space on the Heisenberg group with a…

This is about the paper in the title by Kostaq Hila in Rocky Mt. J. Math. 41, no. 1 (2011), 189-203 for which corrections should be done.

In this paper we establish several Hardy and Hardy-Sobolev type inequalities with homogeneous weights on the first orthant $\displaystyle \mathbb{R}_{*}^n:=\{(x_1, \ldots, x_n):x_1>0, \ldots, x_n>0 \}$. We then use some of them to produce…

This a very brief account of the main line of development of Hardy inequalities.

By the method of coupling and Girsanov transformation, Harnack inequalities [F.-Y. Wang, 1997] and strong Feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a Gelfand…

The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.

This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].

This is a resubmission of preprint 9401008 , which has some TeXnical errors introduced by the "reform" procedure (designed to avoid precisely these problems!). The original can be formatted by editing out the messages "%% following line…

After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this mistake is and how to fix it.

The previous "Polynomial Capacities, Poincare' type inequalities and Spectral synthesis in Sobolev space" is a prerequisite. A parallell reading is recommended.

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates…

This paper has a flaw in an argument that uses the weak-* convergence of measures. The paper was replaced by "Entropy and Its Variational Principle for Locally Compact Metrizable Systems", by the same authors.

We provide a precise statement and self contained proof of a Sobolev inequality (cf. [A, page 236 and page 237]) stated in the original paper. Higher order and fractional inequalities are treated as well.

In the article "Stochastic evolution equations for large portfolios of Stochastic Volatility models" (Arxiv:1701.05640) there is a mistake in the proof of Theorem 3.1. In this erratum we establish a weaker version of this Theorem and then…