Related papers: Makarov's principle for the Bloch unit ball

The Bruss-Robertson inequality gives a bound on the maximal number of elements of a random sample whose sum is less than a specified value, and the extension of that inequality which is given here neither requires the independence of the…

This paper deals with quantitative spectral stability for Aharonov-Bohm operators with many colliding poles of whichever circulation. An equivalent formulation of the eigenvalue problem is derived as a system of two equations with real…

We extend Strichartz's uncertainty principle [18] from the setting of the Sobolov space W 1,2 (R) to more general Besov spaces B 1/p p,1 (R). The main result gives an estimate from below of the trace of a function from the Besov space on a…

Our aim is to establish the first two-parameter version of Bourgain's maximal logarithmic inequality on $L^2(\mathbb R^2)$ for the rational frequencies. We achieve this by introducing a variant of a two-parameter Rademacher--Menschov…

For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $\phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $\displaystyle \phi(\lambda_{1}) \mu(\{x \in \Omega : f(x) \geq…

In this paper we give a generalization and improvement of the Pavlovi\'{c} result on the characterization of continuously differentiable functions in the Bloch space on the unit ball in $\mathbb{R}^m$. Then we derive a Holland--Walsh type…

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…

In this paper, we establish three criteria for the asymptotic behavior of Markov-Feller semigroups. First, we present a criterion for convergence in total variation to a unique invariant measure, requiring only $TV$-eventual continuity of…

We study a new type of extremal problem in complex analysis, referred to as "geometric zero packing", which is the hyperbolic analogue of a problem considered by Abrikosov in the 1950s concerning Bose-Einstein condensates. We relate the…

The maximal minors of a matrix of indeterminates are a universal Gr\"obner basis by a theorem of Bernstein, Sturmfels and Zelevinsky. On the other hand it is known that they are not always a universal Sagbi basis. By an experimental…

We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist…

We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analytic-type smoothness in the infinite-dimensional case where…

The space of Bloch functions on bounded symmetric domains is extended by considering Bloch functions $f$ on the unit ball $B_E$ of finite and infinite dimensional complex Banach spaces in two different ways: by extending the classical Bloch…

This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…

Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have…

The chain rule lies at the heart of the powerful Gamma calculus for Markov diffusions on manifolds, providing remarkable connections between several fundamental notions such as Bakry-\'Emery curvature, entropy decay, and hypercontractivity.…

We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…

Here we obtain explicit formulae for bounds on the complex electrical polarizability at a given frequency of an inclusion with known volume that follow directly from the quasistatic bounds of Bergman and Milton on the effective complex…

We introduce an asymptotic Markov's exponent and show that it is equal to Markov's exponent for a wide class of norms. As a consequence we obtain a lower bound for the optimal exponent in Markov's inequality considered with the norms…