Related papers: Baker Omitted Value

We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…

Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…

The main aim of this paper is to study multidimensional Bohr radii for holomorphic functions defined in complete Reinhardt domains in $\mathbb{C}^n$ with values in complex Banach spaces. More specifically, for holomorphic functions with…

In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we define and study a class of BV functions with zero boundary values. In particular, we show that the class is the closure of…

In this paper, we introduce the notion of the second Bohr radius for vector valued pluriharmonic functions on complete Reinhardt domains in $\mathbb{C}^n$. This investigation is motivated by the work of Lev Aizenberg [Proc. Amer. Math. Soc.…

For each k > 0 we find an explicit function f_k such that the topology of S inside the ball B(p,r) is `bounded' by f_k(r) for every complete Riemannian surface (compact or noncompact) with K\geq -k^2, every point p on the surface, and every…

Let f be a polynomial or a rational function which has r summable critical points. We prove that there exists an r-dimensional manifold in an appropriate space containing f such that for every smooth curve in it through f, the ratio between…

We characterize all logarithmic, holomorphic vector-valued modular forms which can be analytically continued to a region strictly larger than the upper half-plane.

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.

Let $(X, d)$ be a compact metric space, $f: X \to X$ be a continuous transformation with the almost weak specification property and $\varphi: X \to \mathbb{R}$ be a continuous function. We consider the set (called the irregular set for…

In this paper we show that every $L^1$-integrable function on $\partial\Omega$ can be obtained as the trace of a function of bounded variation in $\Omega$ whenever $\Omega$ is a domain with regular boundary $\partial\Omega$ in a doubling…

Let $f$ be a transcendental entire function and let $U$ be a univalent Baker domain of $f$. We prove a new result about the boundary behaviour of conformal maps and use this to show that the non-escaping boundary points of $U$ form a set of…

We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent…

We investigate Baire-one functions whose graph is contained in a graph of usco mapping. We prove in particular that such a function defined on a metric space with values in $\mathbb{R}^d$ is the pointwise limit of a sequence of continuous…

In this article, we study spectral Barron spaces whose elements are made up of some vector-valued functions on a compact group whose Fourier transforms admit a certain summability property. We investigate their functional properties and…

Let $f(z) = \sum_{k=0}^\infty a_k z^k$ be an analytic function in a disk $D_R$ of radius $R>0$, and assume that $f$ is $p$-valent in $D_R$, i.e. it takes each value $c\in{\mathbb C}$ at most $p$ times in $D_R$. We consider its Borel…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

It is proved that any polynomial vector field in two complex variables which is complete on a non-algebraic trajectory is complete.

We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a…