Related papers: The two-weight inequality for the Hilbert transfor…
In this article, we provide two-weight inequalities for the heat flow on the whole space by applying the sparse domination. For power weights, such inequalities were given by several authors. Owing to the sparse domination, we can treat…
This paper explores the connection between a generalized Riesz electric energy and norms on the set of probability measures defined in terms of duality. We derive functional inequalities linking these two notions, recovering and…
Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and…
We examine the level of enhancement that can be achieved in the ZZ and \gamma\gamma channels for a two-Higgs-doublet model Higgs boson (either the light h or the heavy H) with mass near 125 GeV after imposing all constraints from LEP data,…
We analyze the mass spectrum of the charged and neutral Higgs bosons in the framework of two Higgs doublet model (2HDM) in the light of the precision measurement of the $W$ boson mass by the CDF collaboration. We have considered the most…
We prove a quantitative Roth-type theorem for polynomial corners in $\mathbb{R}^2$. Let $P_1$ and $P_2$ be two linearly independent polynomials with zero constant term. We show that any measurable subset of $[0,1]^2$ with positive measure…
Updating various theoretical and experimental constraints on the four different types of two-Higgs-doublet models (2HDMs), we find that only the ``lepton-specific" (or ``type X") 2HDM can explain the present muon g$-$2 anomaly in the…
We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform…
We construct a new realization of type-II seesaw for neutrino masses and baryon asymmetry by extending the standard model with one light and two heavy singlet scalars besides one Higgs triplet. The heavy singlets pick up small vacuum…
On any convex domain in $\mathbb{R}^n$ we can define the Hilbert metric. A projective transformation is an example of an isometry of the Hilbert metric. In this thesis we will prove that the group of projective transformations on a convex…
We discuss the relation between questions regarding the essential normality of finitely generated essentially spherical isometries and some results and conjectures of Arveson and Guo-Wang on the closure of homogeneous ideals in the m-shift…
Suppose $\lambda_1$ and $\lambda_2$ are infinitely divisible Radon measures on real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1} \rightarrow E_{2}$ be a Borel measurable mapping so that $T(\lambda_1) * \rho = \lambda_2 $ for…
Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane such that $\omega$ admits the doubling property $\sup_{0\le r<1}\frac{\int_r^1 \omega(s)\,ds}{\int_{\frac{1+r}{2}}^1 \omega(s)\,ds}<\infty$. Consider the one…
The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the…
We prove that a complete K\"ahler manifold with holomorphic curvature bounded between two negative constants admits a unique complete K\"ahler-Einstein metric. We also show this metric and the Kobayashi-Royden metric are both uniformly…
Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse…
In type II seesaw utilized to explain the observed neutrino masses and mixings, one extends the Standard Model (SM) by introducing scalar fields which transform as a triplet under the electroweak gauge symmetry. New scalar couplings…
We discuss the classification of symmetries and the corresponding symmetry groups in the two-Higgs-doublet model (THDM). We give an easily useable method how to determine the symmetry class and corresponding symmetry group of a given THDM…
An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.
Generalized PT symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state…