Related papers: From dyadic $\Lambda_{\alpha}$ to $\Lambda_{\alpha…
By using the canonical Hamiltonian method, we obtain the mass and entropy of the black holes with general dynamical coupling constant $\lambda$ in Ho\v{r} ava-Lifshitz Gravity. Regardless of whether the horizon is sphere, plane or…
We study gravitational radiation for a positive value of the cosmological constant $\Lambda$. We rely on two battle-tested procedures: (i) We start from the same null coordinate system used by Bondi and Sachs for $\Lambda = 0$, but,…
Let $L= - \mathrm{div} (A \nabla \cdot)$ be an elliptic operator defined on an open subset of $\mathbb{R}^d$, complemented with mixed boundary conditions. Under suitable assumptions on the operator and the geometry, we derive an atomic…
We review bounds for the general Randi\'c index, $R_{\alpha} = \sum_{ij \in E} (d_i d_j)^\alpha$, and use the power mean inequality to prove, for example, that $R_\alpha \ge m\lambda^{2\alpha}$ for $\alpha < 0$, where $\lambda$ is the…
We consider a special symmetric matrix and obtain a similar formula as the one obtained by Weyl's criterion. Some applications of the formula are given, where we give a new way to calculate the integral of $\ln\Gamma(x)$ on $[0,1]$, and we…
Recently we have studied, using a boundary-value approach, quantum amplitudes resulting from gravitational collapse to a black hole. Suitable boundary data for all fields present are posed on initial and final space-like asymptotically flat…
We compute the decay rate of the Standard Model Higgs boson to bottom quarks to order $\alpha\alpha_s$. We apply the optical theorem and calculate the imaginary part of three-loop corrections to the Higgs boson propagator using asymptotic…
The properties of static spherically symmetric black holes, which are both electrically and magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, Lambda, are considered. It is shown that…
In this paper we consider a generalized version of Carleman's inequality. An equivalent version of it states that $\|f\|_{A_\alpha^{2\alpha}}\leq\|f\|_{H^2}$, where $f$ is a holomorphic function and $\alpha>1$. If the norms…
In this paper we give a version of Harris' criterion for determining $H^{1,p}_0$ within $H^{1,p}$ on discrete spaces. Moreover, we provide a converse via Hardy inequalities involving distances to metric boundaries.
A new way to overcome the $\Lambda$ hyperon selective suppression, which is known as the $\Lambda$-anomaly, has been suggested. In particular, the additional radius of a $\Lambda$ hyperon is introduced into the model of hadron resonance gas…
In this survey article some classical results concerning real interpolation between Hardy spaces are briefly presented and then it is explained how those results can be used to establish Yano-type extrapolation theorems for Hardy spaces.…
We introduce a new class of weighted local approximate atoms including classical weighted local atoms. Then we further obtain the weighted local approximate atomic decompositions of weighted local Hardy spaces $h_{\omega} ^p(R^n)$ with…
This article is devoted to a study of the Hardy space $H^{\log} (\mathbb{R}^d)$ introduced by Bonami, Grellier, and Ky. We present an alternative approach to their result relating the product of a function in the real Hardy space $H^1$ and…
We establish a C^1,alpha Schauder estimate of a non-standard degenerate elliptic equation and use it to give another proof of the higher order boundary Harnack inequality. As an application, we obtain the analyticity of the free boundary in…
Let $f \in S_{\kappa}(\Gamma_0(N))$ be a Hecke eigenform at $p$ with eigenvalue $\lambda_f(p)$ for a prime $p$ not dividing $N$. Let $\alpha_p$ and $\beta_p$ be complex numbers satisfying $\alpha_p + \beta_p = \lambda_f(p)$ and $\alpha_p…
Relatively recently it was proved that if $\Gamma$ is an arbitrary set, then any equivalent norm on $c_0(\Gamma)$ can be approximated uniformly on bounded sets by polyhedral norms and $C^\infty$ smooth norms, with arbitrary precision. We…
We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…
In this paper, we first obtain an estimate of the coefficients for $\alpha$-harmonic mappings. By applying these coefficient estimates, we prove the Landau type theorem for $\alpha$-harmonic mappings defined on the unit disc $\ID$.
We give an image characterization of the Poisson transform of L-p functions on the boundary of the exceptional symmetric space by using the Hardy-type norm.