Related papers: Some Bombieri Type Inequalities in Inner Product

A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This result generalises the ones given up to date.

The Cauchy-Schwarz, Buzano and Kre\u{\i}n inequalities are three inequalities about inner product. The main goal of this article is to present refinements of Buzano and Cauchy-Schwarz inequalities, and to present a new proof of a refined…

We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.

In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated…

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

We consider a fairly general class of natural non standard metric products and classify those amongst them, which yield a product of certain type (for instance an inner metric space) for all possible choices of factors of this type (inner…

The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…

We generalize the Beckner's type Poincar\'e inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form $\mu\star\nu$, where $\mu$ is the reference Gaussian measure and $\nu$ is a probability…

We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers-Shephard type…

By using a Hedberg-type inequality, the Adams trace inequality is extended from Lebesgue spaces to product Morrey spaces.

A bilinear inequality of Geba, Greenleaf, Iosevich, Palsson, and Sawyer for the Fourier transform is shown to be equivalent to a simpler linear inequality, and the range of exponents is extended. Related mixed-norm inequalities are…

A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…

We give a formula for the inner product of forms on a Hermitian vector space in terms of linear combinations of iterates of the adjoint of the Lefschetz operator. As an application, we reprove the Kobayashi-Lubke inequality for…

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

A new refinement of the triangle inequality is presented in normed linear spaces. Moreover, a simple characterization of inner product spaces is obtained by using the skew-angular distance.

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

We are proving a Bernstein type inequality in the shift-invariant spaces of $L_2(R)$.

For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…

We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…

We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and…