Related papers: The two-weight inequality for the Hilbert transfor…
Several new properties of weighted Hilbert transform are obtained. If mu is zero, two Plancherel-like equations and the isotropic properties are derived. For mu is real number, a coerciveness is derived and two iterative sequences are…
We give a necessary and sufficient condition for the two weight $L^p$-estimates for paraproducts in non-homogeneous settings, $1<p<\infty$. We are mainly interested in the case $p\ne 2$, since the case $p=2$ is a well-known and easy…
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…
We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under even rotational change of variables on doubling weights. More…
Two-Higgs-doublet models (2HDM) are simple extensions of the Standard Model (SM) where the scalar sector is enlarged by adding a weak doublet. As a result, the Higgs potential depends in general on several free parameters which have to be…
A sufficient condition for the two-weight boundedness of higher order commutators was recently obtained by Holmes and Wick in terms of an intersection of two BMO spaces. We provide an alternative proof, showing that the higher order case…
In the paper we study the existence of balanced metrics of Hodge-Riemann type on non-K\"ahler complex manifolds. We first find some general obstructions, for instance that a Hodge-Riemann balanced manifold of complex dimension $n$ has to be…
This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these…
Assuming the bilinear reverse Holder's condition, we character weighted inequalities for the bilinear maximal operator on filtered measure spaces. We also obtain Hytonen-Perez type weighted estimates for the bilinear maximal operator. Our…
We propose a solution to the recent $W$ mass measurement by embedding the Standard Model within $E_6$ models. The presence of a new $U(1)$ group shifts the $W$ boson mass at the tree level and introduces a new gauge boson $Z^{\prime}$ which…
Consider a Hilbert space obtained as the completion of the polynomials C[z} in m-variables for which the mnonomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same…
We present ten different characterizations of functions satisfying a weak reverse H\"older inequality on an open subset of a metric measure space with a doubling measure. Among others, we describe these functions as a class of weak…
Bell's inequality plays an important role with respect to the Einsteinian question about the physical reality of quantum theory. While Bell's inequality is usually viewed within the geometric framework of a Hilbert space quantum model, the…
We establish Zaremba problem for Laplacian and $p$-Laplacian with degenerate weights when the Dirichlet condition is only imposed in a set of positive weighted capacity. We prove weighted Sobolev-Poincar\'{e} inequality with sharp…
In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series…
The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan…
This is the first part of a series of three articles. In this paper, we obtain weighted norm inequalities for different conical square functions associated with the Heat and the Poisson semigroups generated by a second order divergence form…
Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions…
We show that a suitable Slater condition implies a duality inequality between the Hoffman constants of the following feasibility problems: $$ \begin{array}{r} Ax-b \in S\\ x \in R \end{array} \qquad\text{ and }\qquad \begin{array}{r} c-A^T…
We study the properties of reflectionless measures for a Calder\'{o}n-Zygmund operator T. Roughly speaking, these are measures $\mu$ for which T(\mu) vanishes (in a weak sense) on the support of the measure. We describe the relationship…