Related papers: Inner functions in weak Besov spaces

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs…

We show that analytic analogs of Brunn-Minkowski-type inequalities fail for functional intrinsic volumes on convex functions. This is demonstrated both through counterexamples and by connecting the problem to results of Colesanti, Hug, and…

Let $\mathcal H$ be the Drury-Arveson or Dirichlet space of the unit ball of $\mathbb C^d$. The weak product $\mathcal H\odot\mathcal H$ of $\mathcal H$ is the collection of all functions $h$ that can be written as $h=\sum_{n=1}^\infty f_n…

We give a necessary and sufficient condition for the convergence of an infinite product of rational inner functions on the polydisk, and explore generalization to the polydisk of Malmquist- Takenaka bases and various versions of unwinding

In this paper, we extend the definition of hyperinner product defined on weak hypervector spaces with a hyperoperation scalar product to weak hypervector spaces with the hyperoperations sum and scalar products.

For locally convex spaces, we systematize several known equivalent definitions of Fr\'echet (G\^ ateaux) Differentiability Spaces and Asplund (Weak Asplund) Spaces. As an application, we extend the classical Mazur's theorem as follows: Let…

In this paper, by using the atomic decomposition theory of weighted Hardy spaces, we will give some weighted weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and…

We give an intrinsic characterization of the restrictions of Sobolev, Triebel-Lizorkin and Besov spaces to regular subsets of $R^n$ via sharp maximal functions and local approximations.

We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…

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…

Within the new concept of a local iterated function system (local IFS), we consider a class of attractors of such IFSs, namely those that are graphs of functions. These new functions are called local fractal functions and they extend and…

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 $H^2 \ominus BH^2$…

A Bochner integral formula is derived that represents a function in terms of weights and a parametrized family of functions. Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are…

We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…

Entropy functionals (i.e. convex integral functionals) and extensions of these functionals are minimized on convex sets. This paper is aimed at reducing as much as possible the assumptions on the constraint set. Dual equalities and…

Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.

We investigate the internal space of Bessel functions which is associated to the group Z of positive and negative integers defining their orders. As a result we propose and prove a new unifying formula (to be added to the huge literature on…

This article gives dual representations for convex integral functionals on the linear space of regular processes. This space turns out to be a Banach space containing many more familiar classes of stochastic processes and its dual can be…

We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…

We study spaces $\mathcal{CV}^{k}(\Omega,E)$ of $k$-times continuously partially differentiable functions on an open set $\Omega\subset\mathbb{R}^{d}$ with values in a locally convex Hausdorff space $E$. The space…