Related papers: Identifying Bergman space functions from intervals

We unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $\mathbb{R}^2$). We show how the unit ball…

We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V=M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2_\omega$ of the function $z \mapsto a-z$…

The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are…

More precise estimates for the Bergman metric on strongly pseudoconvex domains are given, based on the use of the squeezing function.

This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…

We study $BV$ functions in a Hilbert space $X$ endowed with a probability measure $\nu$, assuming that $\nu$ is Fomin differentiable along suitable directions. We establish basic characterizations, and we apply the general theory to…

In this survey, we consider Banach spaces of analytic functions in one and several complex variables for which: (i) polynomials are dense, (ii) point-evaluations on the domain are bounded linear functionals, and (iii) the shift operator…

We present a collection of observations concerning the peculiar behavior of the Lebesgue function in the setting of the interval $[-1,1]\subset \mathbb{R}$ and the square $[-1,1]^2\subset \mathbb{R}^2$. We provide numerical results and…

We prove that any given function can be smoothly approximated by functions lying in the kernel of a linear operator involving at least one fractional component. The setting in which we work is very general, since it takes into account…

We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.

We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from $L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcal B_0$ are onto. We…

In this article, we study the properties of a class of functional spaces which arise from the investigation of nonlinear differential equations. We establish some integral inequalities then by applying these inequalities, we prove some…

We define the harmonic Bergman space on locally finite trees with respect to a suitable probabilistic Laplacian and a class of weighted flow measures. We characterise the corresponding Bergman projection and prove that it is bounded on…

We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.

We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier…

We develop a version of Herbrand's theorem for continuous logic and use it to prove that definable functions in infinite-dimensional Hilbert spaces are piecewise approximable by affine functions. We obtain similar results for definable…

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.

We determine precisely when the Bergman projection $P_\beta$ is bound\-ed from Lebesgue spaces $L^p_\alpha$ to weighted Bergman spaces $\mathcal B^p_\alpha$ of $\mathcal H$-harmonic functions on the hyperbolic ball, and verify a recent…

By mean of generalized Fourier series and Parseval's equality in weighted $L^{2}$--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp…

We investigate several boundedness properties of function spaces considered as uniform spaces.