Related papers: On Some Double-Series Inequalities
Let M be an N-function satisfying the $\Delta_2$- condition, let $\omega, \vp$ be two other functions, $\omega\ge 0$. We study Hardy-type inequalities \[ \int_{\rp} M(\omega (x)|u(x)|) {\rm exp}(-\vp (x))dx \le C\int_{\rp} M(|u'(x)|) {\rm…
We are going to classify sets by a given mean in two ways. Firstly we study small and big sets regarding a given mean. Secondly we study sets that have the same weight according to a mean. We also generalize the notion of roundness and get…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\geq0$) and best constant $\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\alpha,\infty)$. We apply this to…
In this talk, some aspects of duality symmetries are presented.
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
In this note, we investigate the sharpness of existing bounds for various types of bi-parameter paraproducts acting between product Hardy spaces in the dyadic setting. We show that these bounds are sharp in most cases but fail to be so in…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on $n$-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions $n \in…
In the paper, using the language of spin-half particles, Hardy's paradox is examined within different semantics: a partial one, a many-valued one, and one defined as a set of weak values of projection operators. As it is shown in this…
In this paper, we derive a new proof on some sharp double integral inequalities of the Hermite-Hadamard type. Our approach is mainly based on well-known Taylor's theorem with the integral remainder.
The main purpose of this article is to obtain (weighted) fractional Hardy inequalities with a remainder and fractional Hardy-Sobolev-Maz'ya inequalities valid for $1<p<2$.
We improve the classical discrete Hardy inequality for $ 1<p<\infty $ for functions on the natural numbers. For integer values of $ p $ the Hardy weight is an absolutely monotonic function.
In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.
Some inequalities for different types of convexity are established.
This work discusses self-improving properties of the Muckenhoupt condition and weighted norm inequalities for the Hardy-Littlewood maximal function on metric measure spaces with a doubling measure. Our main result provides direct proofs of…
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…