相关论文: Hardy-type Inequalities Via Auxiliary Sequences

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

Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…

We show how to fill "countable" gaps in Hardy fields. We use this to prove that any two maximal Hardy fields are back-and-forth equivalent.

We look at thin interpolating sequences and the role they play in uniform algebras, Hardy spaces, and model spaces.

We derive a number of equivalent criterions for the variable exponent Hardy type inequality |\frac{1}{x}\int_{0}^{x}f(t)dt|_{L^{p(.)}(0,1)}\leq C|f|_{L^{p(.)}(0,1)}; f\geq 0. to hold, whenever the exponent $p:(0,1)\to (1,\infty)$ is…

We present a simple method for proving Rellich inequalities on Riemannian manifolds with constant, non-positive sectional curvature. The method is built upon simple convexity arguments, integration by parts, and the so-called Riccati pairs,…

We prove that a pointwise fractional Hardy inequality implies a fractional Hardy inequality, defined via a Gagliardo-type seminorm. The proof consists of two main parts. The first one is to characterize the pointwise fractional Hardy…

We extend Hardy's inequality from sequences of non-negative numbers to sequences of positive semi-definite operators if the parameter p satisfies 1<p<=2, and to operators under a trace for arbitrary p>1. Applications to trace functions are…

Using elementary techniques, we prove sharp anisotropic Hardy-Littlewood inequalities for positive multilinear forms. In particular, we recover an inequality proved by F. Bayart in 2018.

We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on R. This work refines the results that…

Considering some parameters and by means of an inequality of Hadamard, we derive general half-discrete Hilbert-type inequalities. Then we highlight some special cases.

We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part an anisotropic operator, a Hardy-type potential, and a…

We deal with Dirac operators with external homogeneous magnetic fields. Hardy-type inequalities related to these operators are investigated: for a suitable class of transversal magnetic fields, we prove a Hardy inequality with the same best…

Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…

We prove a two dimensional Holder and reverse-Holder inequality on time scales via the diamond-alpha integral. Other integral inequalities are established as well, which have as corollaries some recent proved Hardy-type inequalities on time…

We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…

We count integer points on bihomogeneous varieties using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in…

A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…

We give a simple proof of Hardy's inequality, based on the logarithmic Caccioppoli estimate for p-superharmonic functions in several variables.

We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…