Related papers: Double logarithmic inequality with a sharp constan…

We prove a Leibniz rule for BV functions in a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality. Unlike in previous versions of the rule, we do not assume the functions to be locally…

We present some monotonicity results for Dirichlet $L$-functions associated to real primitive characters. We show in particular that these Dirichlet $L$-functions are far from being logarithmically completely monotonic. Also, we show that,…

We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…

In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.

The inverse tangent function can be bounded by different inequalities, for example by Shafer's inequality. In this publication, we propose a new sharp double inequality, consisting of a lower and an upper bound, for the inverse tangent…

A version of the recent functional inequality between the Hessians of the square root and the logarithm of positive functions is proven in spaces with non-zero curvature.

In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…

We review and formulate results concerning log-concavity and strong-log-concavity in both discrete and continuous settings. We show how preservation of log-concavity and strongly log-concavity on $\mathbb{R}$ under convolution follows from…

We show that the two-weight estimate for the dyadic square function proved by Lacey--Li in [2] is sharp.

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for…

We introduce and study a log discrepancy function on the space of semivaluations centered on an integral noetherian scheme of positive characteristic. Our definition shares many properties with the analogue in characteristic zero; we prove…

In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin-Fourier (Walsh-Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in…

A logarithmic type Lieb-Thirring inequality for two-dimensional Schroedinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.

We show that the sharp constant in the classical $n$-dimensional Hardy-Leray inequality can be improved for axisymmetric divergence-free fields, and find its optimal value. The same result is obtained for $n=2$ without the axisymmetry…

In the paper, we establish an inequality involving the gamma and digamma functions and use it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.

We prove sharp version of Riesz-Fej\'er inequality for functions in harmonic Hardy space $h^p(\mathbb{D})$ on the unit disk $\mathbb{D}$, for $p>1,$ thus extending the result from \cite{KPK} and resolving the posed conjecture.

We show that the derivative of a log-analytic function is log-analytic. We prove that log-analytic functions exhibit strong quasianalytic properties. We establish the parametric version of Tamm's theorem for log-analytic functions.

We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has {\em unit determinant}. Our result…

We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.

We find the sharp constants $C_p$ and the sharp functions $C_p=C_p(x)$ in the inequality $$|u(x)|\leq \frac{C_p}{(1-|x|^2)^{(n-1)/p}}\|u\|_{h^p(B^n)}, u\in h^p(B^n), x\in B^n,$$ in terms of Gauss hypergeometric and Euler functions. This…