ترغب بنشر مسار تعليمي؟ اضغط هنا

Transport proofs of some functional inverse Santal{o} inequalities

60   0   0.0 ( 0 )
 نشر من قبل Simon Zugmeyer
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we present a simple proof of a recent result of the second author which establishes that functional inverse-Santal{o} inequalities follow from Entropy-Transport inequalities. Then, using transport arguments together with elementary correlation inequalities, we prove these sharp Entropy-Transport inequalities in dimension 1. We also revisit the proof of the functional inverse-Santal{o} inequalities in the n dimensional unconditional case using these ideas.

قيم البحث

اقرأ أيضاً

Let $f in M_+(mathbb{R}_+)$, the class of nonnegative, Lebesgure-measurable functions on $mathbb{R}_+=(0, infty)$. We deal with integral operators of the form [ (T_Kf)(x)=int_{mathbb{R}_+}K(x,y)f(y), dy, quad x in mathbb{R}_+, ] with $K in M_+(mathbb{R}_+^2)$.
In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities include Hardy, Rellich, Hardy-Littllewood-Sobolev, Galiardo-Nirenber g, Caffarelli-Kohn-Nirenberg and Trudinger-Moser inequalities. Some of these estimates have been known in the case of the sub-Laplacians, however, for more general hypoelliptic operators almost all of them appear to be new as no approaches for obtaining such estimates have been available. Moreover, we obtain sever
We survey some classical norm inequalities of Hardy, Kallman, Kato, Kolmogorov, Landau, Littlewood, and Rota of the type [ |A f|_{mathcal{X}}^2 leq C |f|_{mathcal{X}} big|A^2 fbig|_{mathcal{X}}, quad f in dombig(A^2big), ] and recall that under excee dingly stronger hypotheses on the operator $A$ and/or the Banach space $mathcal{X}$, the optimal constant $C$ in these inequalities diminishes from $4$ (e.g., when $A$ is the generator of a $C_0$ contraction semigroup on a Banach space $mathcal{X}$) all the way down to $1$ (e.g., when $A$ is a symmetric operator on a Hilbert space $mathcal{H}$). We also survey some results in connection with an extension of the Hardy-Littlewood inequality involving quadratic forms as initiated by Everitt.
228 - Bo-Yan Xi , Fuzhen Zhang 2021
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus inequalities. Our results are stronger and more general than the existing ones.
We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure $sigma$, we prove functional integral inequalities with respect to $sigma$, such as logarithmic Sobolev and Poincar{e} type. Consequently, some i ntegrability properties of exponential functions with respect to $sigma$ are deduced.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا