Related papers: On weighted Poincar\'e inequalities

In this note we prove a weighted version of the Khintchine inequalities.

Weighted fractional Poincar\'e-type inequalities are proved on John domains whenever the weights defined on the domain are depending on the distance to the boundary and to an arbitrary compact set in the boundary of the domain.

In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.

We prove a fractional version of Poincar\'e inequalities in the context of $\R^n$ endowed with a fairly general measure. Namely we prove a control of an $L^2$ norm by a non local quantity, which plays the role of the gradient in the…

In this note we prove Poincar\'e type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We investigate the character of the linear constraints which are needed for Poincar\'e and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a…

The main result of this paper supports a conjecture by C. P\'erez and E. Rela about a very recent result of theirs on self-improving theory. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our…

We obtain new sharp weighted Poincar{\'e} inequalities on Riemannian manifolds for a general class of measures. When specialised to generalised Cauchy measures, this gives a unified and simple proof of the weighted Poincar{\'e} inequality…

We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…

In this short communication, we present a new proof for the Korn inequality in a n-dimensional context. The results are based on standard tools of real and functional analysis. For the final result the standard Poincar\'{e} inequality plays…

In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…

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 study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…

We obtain simple proofs of certain inequalites for bivariate means.

We characterize the real interpolation space between weighted $L^1$ and $W^{1,1}$ spaces on arbitrary domains different from $\mathbb{R}^n$, when the weights are positive powers of the distance to the boundary multiplied by an $A_1$ weight.…

In this paper we will study the equivalence between super-Poincar\'e inequality and some log-Sobolev type inequalities, including weak log-Sobolev inequality and super log-Sobolev inequality. The explicit relations between associated rate…

This set of notes re-proves known results on weighted automata (over a field, also known as multiplicity automata). The text offers a unified view on theorems and proofs that have appeared in the literature over decades and were written in…

We show some non-standard Poincar\'e type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional…

We introduce a simple criterion to check coercivity of bilinear forms on subspaces of Hilbert-spaces and Banach-spaces. The presented criterion allows to derive many standard and non-standard variants of Poincar\'e- and Friedrichs-type…