We prove a range of $$L^p$$ bounds for singular Brascamp–Lieb forms with cubical structure. pass through sparse and local bounds, the latter proved by an iteration Fourier expansion, telescoping, Cauchy–Schwarz inequality. allow $$2^{m-1}<p\le \infty $$ m dimension cube, extending earlier result that required $$p=2^m$$ . The threshold $$2^{m-1}$$ is sharp in our theorems.

Abstract The orbit space for a scalar field in complex square matrix representation obtains Minkowski structure from the Cauchy–Schwarz inequality. It can be used to find vacuum stability conditions and minima of potential. method is suitable fields such as bidoublet, an SU (2) triplet or (3) octet. We use formalism left-right symmetric potential bidoublet left right Higgs doublets.

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of relation. This is achieved strengthening celebrated Cauchy–Schwarz inequality using a method brackets convex functions. The outperform several relations, notably better than some recent best lower bounds such as [Phys. Rev. Lett. 120, 230402 (2018)] A...

In this work, a refinement of the Cauchy–Schwarz inequality in inner product space is proved. A more general Kato’s or so called mixed Schwarz established. Refinements some famous numerical radius inequalities are also pointed out. As shown these refinements generalize and refine recent old results obtained literature. Among others, it proved that if $$T\in \mathscr {B}\left( {H}\right) $$ , th...

This present work aims to ameliorate the celebrated Cauchy-Schwarz inequality and provide several new consequences associated with numerical radius upper bounds of Hilbert space operators. More precisely, for arbitrary a, b ? H 0, we show that |?a,b?|2 1 + ?a??b?|?a, b?| ?/?+1 ?a?2?b?2 ?a?2?b?2. As a consequence, refine generalize some Kittaneh?s results in [A an estimate Frobenius companion ma...

Let L(H) denote the C∗-algebra of adjointable operators on a Hilbert C∗-module H. In this paper, we introduce generalized Cauchy–Schwarz inequality for in L(H). More precisely, an operator A∈L(H) is said to satisfy if there exists ν∈(0,1) such that ‖⟨Ax,y⟩‖≤(‖Ax‖‖y‖)ν(‖Ay‖‖x‖)1−ν(x,y∈H).We investigate various properties which inequality. particular, prove A satisfies has polar decomposition, th...