Related papers: Inner Functions in certain Hardy-Sobolev Spaces

A necessary and sufficient condition for an inner function F in the upper half-plane (UHP) to satisfy F = E*/E where E is a de Branges function is presented. Since F_E =E^*/E is an inner function for any de Branges function E, and the map…

Assuming the negative part of the potential is uniformly locally $L^1$, we prove a pointwise $L^p$ estimate on derivatives of eigenfunctions of one-dimensional Schrodinger operators. In particular, if an eigenfunction is in $L^p$, then so…

We study a concept of inner function suited to Dirichlet-type spaces. We characterize Dirichlet-inner functions as those for which both the space and multiplier norms are equal to 1.

We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…

Let $\Omega\subset\mathbb{C}^n$ be a strictly pseudoconvex Runge domain with $C^2$-smooth defining function, $l\in\mathbb{N},$ $p\in(1,\infty).$ We prove that the holomorphic function $f$ has derivatives of order $l$ in $H^p(\Omega)$ if and…

We give a systematic study on the Hardy spaces of functions with values in the non-commutative $L^p$-spaces associated with a semifinite von Neumann algebra ${\cal}M.$ This is motivated by the works on matrix valued Harmonic Analysis…

Suppose $\alpha,\beta \in \mathbb{R}\backslash \mathbb{Z}^-$ such that $\alpha+\beta>-1$ and $1\leq p \leq \infty$. Let $u=P_{\alpha,\beta}[f]$ be an $(\alpha,\beta)$-harmonic mapping on $\mathbb{D}$, the unit disc of $\mathbb{C}$, with the…

We investigate the Hardy space $H^1_L$ associated with a self-adjoint operator $L$ defined in a general setting in [S. Hofmann, et. al., Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates,…

We show that inner functions are extreme points of the unit ball of the Hardy-Lorentz space $H(\Lambda(\varphi))$, for $\Lambda(\varphi)$ a Lorentz space with $\varphi$ strictly increasing and strictly concave.

Let ${\mathcal X}$ be an RD-space, which means that ${\mathcal X}$ is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in ${\mathcal X}$. In this paper, the…

Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour. However, there are natural examples where one finds a mix of both behaviour (locally Gaussian and…

Let $n\ge 1$ and $\varphi: \mathbb{D}^n\to\mathbb{D}$ be a holomorphic function, where $\mathbb{D}$ denotes the open unit disk of $\mathbb{C}$. Let $\Theta: \mathbb{D} \to \mathbb{D}$ be an inner function and $K^p_\Theta$, $p>0$, denote the…

The Hardy spaces for Fourier integral operators $\mathcal{H}_{FIO}^{p}(\mathbb{R}^{n})$, for $1\leq p\leq \infty$, were introduced by Smith in [Smith,1998] and Hassell et al. in [Hassell-Portal-Rozendaal,2020]. In this article, we give…

Let $1\leq p<\infty$, $\alpha>-1$, and let $\varphi$ be a measurable function on $(0,\infty)$. The main purpose of this paper is to study the Hausdorff operator \[ \mathscr H_\varphi f(z)=\int_0^\infty f\left(\frac{z}{t}\right)…

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

A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions…

It is studied that pointwise estimates and continuities on Hardy spaces of pseudo-differential operators (PDOs for short) with the symbol in general H\"{o}rmander's classes. We get weighted weak-type $(1,1)$ estimate, weighted normal…

The Hausdorff dimension of the graphs of the functions in H\"older and Besov spaces (in this case with integrability p \geq 1) on fractal d-sets is studied. Denoting by s \in (0,1] the smoothness parameter, the sharp upper bound…

The $L^p$-cosine transform of an even, continuous function $f\in C_e(\Sn)$ is defined by: $$H(x)=\int_{\Sn}|\ip{x}{\xi}|^pf(\xi) d\xi,\quad x\in {\R}^n.$$ It is shown that if $p$ is not an even integer then all partial derivatives of even…

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…