Related papers: Inner Functions with Derivatives in the Weak Hardy…
It is shown that inner functions in weak Besov spaces are precisely the exponential Blaschke products.
Inner functions play a central role in function theory and operator theory on the Hardy space over the unit disk. Motivated by recent works of C. B\'en\'eteau et al. and of D. Seco, we discuss inner functions on more general weighted Hardy…
We give a generalization of the notion of finite Blaschke products from the perspective of generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these functions relate to the so-called…
The relationship between the distribution of zeros of an infinite Blaschke product $B$ and the inclusion in weighted Bergman spaces $A_{\alpha}^p$ of the derivative of $B$ or the derivative of functions in its model space $H^2 \ominus BH^2$…
For $1/2<p<1$, a description of inner functions whose derivative is in the Hardy space $H^p$ is given in terms of either their mapping properties or the geometric distribution of their zeros.
By classical results of Herglotz and F. Riesz, any bounded analytic function in the complex unit disk has a unique inner-outer factorization. Here, a bounded analytic function is called \emph{inner} or \emph{outer} if multiplication by this…
We define as a distribution the product of a function (or distribution) h in some Hardy space Hp with a function b in the dual space of Hp. Moreover, we prove that the product bxh may be written as the sum of an integrable function with a…
We study the rate of growth of some integral means of the derivatives of a Blaschke product and we generalize several classical results. Moreover, we obtain the rate of growth of integral means of the derivative of functions in the model…
We consider the classical problem of maximizing the derivative at a fixed point over the set of all bounded analytic functions in the unit disk with prescribed critical points. We show that the extremal function is essentially unique and…
A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of the derivative of this map reflect the geometry of the Blaschke product. We identify two classes of extremal Blaschke…
We derive lower bounds in best rational approximation of given degree to finite Blaschke products, in the Hardy space $H^2$ of the unit disk. We first consider approximation to $z^N$, and then move on to more general Blaschke products whose…
Recently, several papers have considered a nonlinear analogue of Fourier series in signal analysis, referred to as either nonlinear phase unwinding or adaptive Fourier decomposition. In these processes, a signal is represented as the real…
We obtain an upper bound for the derivative of a Blaschke product, whose zeros lie in a certain Stolz-type region. We show that the derivative belongs to the space of analytic functions in the unit disk, introduced recently in \cite{FG}. As…
This paper deals with representing in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces $H^p(\bb D^n) \ (1\le p\le \infty)$ that remain invariant under the action of coordinate wise multiplication by an…
We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of…
We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such…
Let $\mathscr{H}^2$ denote the space of ordinary Dirichlet series with square summable coefficients, and let $\mathscr{H}^2_0$ denote its subspace consisting of series vanishing at $+\infty$. We investigate the weak product spaces…
A broader class of Hardy spaces and Lebesgue spaces have been introduced recently on the unit circle by considering continuous $\|.\|_1$-dominating normalized gauge norms instead of the classical norms on measurable functions and a Beurling…
In this paper, we will discuss the space of functions of weak bounded mean oscillation. In particular, we will show that this space is the dual space of the special atom space, whose dual space was already known to be the space of…
We characterize the connected components of the subset $\cni$ of $H^\infty$ formed by the products $bh$, where $b$ is Carleson-Newman Blaschke product and $h\in H^\infty$ is an invertible function. We use this result to show that, except…