Related papers: Sharp anisotropic Hardy--Littlewood inequality for…

We prove an appropriate sharp quantitative reverse H\"older inequality for the $C_p$ class of weights from which we obtain as a limiting case the sharp reverse H\"older inequality for the $A_\infty$ class of weights. We use this result to…

Some q-analysis variants of Hardy type inequalities of the form \int_0^b (x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_qt)^p d_qx \leq C \int_0^b f^p(t) d_qt with sharp constant C are proved and discussed. A similar result with the…

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…

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…

By a systematic development of fundamental concepts of conformable calculus we establish conformable divergence theorem and Green's identities which we combine with some new anisotropic Picone type identities to derive a generalized…

We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type…

We prove a weighted Sobolev inequality and a Hardy inequality on manifolds with nonnegative Ricci curvature satisfying an inverse doubling volume condition. It enables us to obtain rigidity results for Ricci flat manifolds, generalizing…

The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.

We prove all the maximizers of the sharp Hardy-Littlewood-Sobolev inequality are smooth. More generally, we show all the nonnegative critical functions are smooth, radial with respect to some points and strictly decreasing in the radial…

In this paper we establish sharp weighted Hardy type inequalities on the Carnot group with homogeneous dimension $Q\ge 3$.

We give a simple proof of the $\lambda = d-2$ cases of the sharp Hardy-Littlewood-Sobolev inequality for $d\geq 3$, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for $d=2$ via a monotone flow governed by the fast diffusion…

New Hardy type inequalities in sectorial area and as a limit in an exterior of a ball are proved. Sharpness of the inequalities is shown as well.

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a non-linear and non-local version of the ground state representation.

We establish a bipolar Hardy inequality on complete, not necessarily reversible Finsler manifolds. We show that our result strongly depends on the geometry of the Finsler structure, namely on the reversibility constant $r_F$ and the…

The Hardy--Littlewood inequalities on $\ell _{p}$ spaces provide optimal exponents for some classes of inequalities for bilinear forms on $\ell _{p}$ spaces. In this paper we investigate in detail the exponents involved in Hardy--Littlewood…

We study sharp $p$-variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We also use computational assistance to find sharp constants in…

We show that the $\Lp$ Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg…

The sharp trace inequality of Jose Escobar is extended to traces for the fractional Laplacian on R^n and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb's sharp form of…

In this paper we shall prove a sharpened version of the Finsler-Hadwiger inequality which is a strong generalization of Weitzenbock inequality. After that we give another refinement of this inequality and in the final part we provide some…

We give the full solution of the following problem: obtain sharp inequalities between the moduli of smoothness $\omega_\alpha(f,t)_q$ and $\omega_\beta(f,t)_p$ for $0<p<q\le \infty$. A similar problem for the generalized $K$-functionals and…