相关论文: Eigenvalue extensions of Bohr's inequality
Aharonov-Albert-Vaidman's weak values are investigated by a semiclassical method. Examples of the semiclassical calculation that reproduces "anomalous" weak values are shown. Furthermore, a complex extension of Ehrenfest's quantum-classical…
We prove the self-improving property of very weak solutions to non-uniformly elliptic problems of double phase type in divergence form under sharp assumptions on the nonlinearity.
In this article, we study Bohr-type inequalities involving a parameter or convex combinations for $K$-quasiconformal, sense-preserving harmonic mappings in $\mathbb{D}$, where the analytic part is subordinate to a convex function. Moreover,…
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
In this corrigendum, we offer a correction to [J. Korean. Math. Soc., 54 (2017), pp. 461--477]. We construct a counterexample for the strengthened Cauchy--Schwarz inequality used in the original paper. In addition, we provide a new proof…
We give new proofs that some Banach spaces have Pe{\l}czy\'nski's property $(V)$.
By employing harmonic analysis techniques, we derive weak-type Caffarelli-Kohn-Nirenberg inequalities under natural parameter conditions. A key feature of these weak-type versions is that they remain valid even at critical parameter values…
We will present an estimate for the first eigenvalue of the Dirichlet and Neumann problems in terms of the Bakry-\'Emery Ricci curvature for a compact weighted manifold. As an application we will establish a stability condition for a…
For rational points on algebraic varieties defined over a number field $K$, we study the behavior of the property of weak approximation with Brauer-Manin obstruction under extension of the ground field. We construct K-varieties accompanied…
In this work we investigate a very weak solution to the initial-boundary value problem of an Euler-Bernoulli beam model. We allow for bending stiffness, axial- and transversal forces as well as for initial conditions to be irregular…
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance…
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide a useful amplification…
We establish the converse of Weyl's eigenvalue inequality for additive Hermitian perturbations of a Hermitian matrix.
In this paper we prove the Stein-Weiss inequality in variable exponent Morrey spaces over a bounded domain. Our work extends earlier results in the variable exponent Lebesgue and Morrey settings, and utilizes new proof techniques applicable…
We prove existence and comparison results for multi-valued variational inequalities in a bounded domain $\Omega$ of the form \begin{equation*} u\in K\,:\, 0 \in Au+\partial I_K(u)+\mathcal{F}(u)+\mathcal{F}_\Gamma(u)\quad\text{in…
This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see $(KC)$ below). We use the variational method in the light of Moser-Trudinger inequality to show the existence of weak…
In this paper we improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequality connected to the M\"obius function, derived by Helfgott in…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals…
We obtain simple proofs of certain inequalites for bivariate means.