By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy’s nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocal...

We address the question of exact controllability of the wave and Schrödinger equations perturbed by a singular inverse-square potential. Exact boundary controllability is proved in the range of subcritical coefficients of the singular potential and under suitable geometric conditions. The proof relies on the method of multipliers. The key point in the proof of the observability inequality is a ...

We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on the space of CRpluriharmonic functions. We will then obtain the sharp Beckner-Onofri inequality for CR-pluriharmonic functions on the sphere, and, as a consequence, a sharp logarithmic Hardy-Littlewood-Sobolev inequali...

Abstract By the use of weight coefficients and techniques real analysis, we establish a new Hardy–Mulholland-type inequality with mixed kernel best possible constant factor in terms hypergeometric function. Equivalent forms, an operator expression norm reverses are also considered.

We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d≥3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.

We give a short summary of Varopoulos’ generalised Hardy-LittlewoodSobolev inequality for self-adjoint C0 semigroups and give a new probabilistic representation of the classical fractional integral operators on Rn as projections of martingale transforms. Using this formula we derive a new proof of the classical Hardy-LittlewoodSobolev inequality based on Burkholder-Gundy and Doob’s inequalities...

Abstract In this paper, by virtue of the symmetry principle, applying techniques real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients use them to establish a reverse extended Hardy–Hilbert’s inequality with multi-parameters. Then, obtain equivalent forms some statements best possible constant factor related several parameters. Finally, illustrate how obta...

We prove new Hardy–Copson-type (γ,a)-nabla fractional dynamic inequalities on time scales. Our results are proven by using Keller’s chain rule, the integration parts formula, and Hölder inequality When γ=1, then we obtain some well-known time-scale due to Hardy. As special cases, continuous discrete inequalities. Symmetry plays an essential role in determining correct methods solve