Related papers: Multipliers on bi-parameter Haar system Hardy spac…

We extend several fundamental estimates regarding spectral multipliers for the free Laplacian on $\mathbb R^3$ to the case of perturbed Hamiltonians of the form $H=-\Delta+V$, where $V$ is a scalar real-valued potential. Results include…

Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $\sigma$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual…

This paper generalizes the classical Sz.-Nagy--Foias $H^{\infty}(\mathbb{D})$ functional calculus for Hilbert space contractions. In particular, we replace the single contraction $T$ with a tuple $T=(T_1, \dots, T_d)$ of commuting bounded…

In this paper we compare various classes of Schur multipliers: classical matrix Schur multipliers, discrete Schur multipliers, Schur multipliers with respect to measures and Schur multipliers with respect to spectral measures. The main…

We prove several results about functions which preserve the Schur-Agler class under Hadamard or coefficient-wise product. First, functions which preserve the Schur class necessarily preserve the Schur-Agler class. Second, ``moments'' of…

In this paper we study Hardy spaces associated with non-negative self-adjoint operators and develop their vector-valued theory. The complex interpolation scales of vector-valued tent spaces and Hardy spaces are extended to the endpoint p=1.…

Let $T = (T_1, \ldots, T_n)$ be a commuting tuple of bounded linear operators on a Hilbert space $\mathcal{H}$. The multiplicity of $T$ is the cardinality of a minimal generating set with respect to $T$. In this paper, we establish an…

We show that for two doubling measures $\sigma$ and $\omega$ on $\mathbb{R}^{n}$ and any fixed dyadic grid $\mathcal{D}$ in $\mathbb{R}^{n}$, \[ \mathfrak{N}_{\mathbf{R}^{\lambda, n}}\left( \sigma,\omega\right)…

Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0…

This paper discusses the two classical Hardy operators $\mathcal{H}_{1}$ on $L^2(0, 1)$ and $\mathcal{H}_{\infty}$ on $L^2(0, \infty)$ initially studied by Brown, Halmos and Shields. Particular emphasis is given to the construction of…

We introduce the notion of characteristic functions for commuting tuples of hypercontractions on Hilbert spaces, as a generalization of the notion of Sz.-Nagy and Foias characteristic functions of contractions. We present an explicit method…

In this article, the authors consider the Schr\"{o}dinger type operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$, where the matrix $A$ is symmetric and satisfies uniformly elliptic condition and the nonnegative potential…

In this paper, certain classes of Hilbert spaces of Dirichlet series with weighted norms and their corresponding multiplier algebras will be explored. For a sequence $\{w_n\}_{n=n_0}^\infty $ of positive numbers, define \[\mathcal…

This paper consists in a first study of the Hardy space H1 in the rational Dunkl setting. Following Uchiyama's approach, we characterizee H1 atomically and by means of the heat maximal operator. We also obtain a Fourier multiplier theorem…

In this paper, we investigate contractive projections, conditional expectations, and idempotent coefficient multipliers on the Hardy spaces $H^p(\mathbb{T})$ for $0<p<1$. For such values of $p$, we first establish a general extension…

This paper is devoted to the equivalence of various characterizations of holomorphic $H^1$ Hardy spaces on tube domains over polyhedral cones. We establish a new iterated Poisson integral formula which reproduces holomorphic functions on…

Let S be the semidirect product of R^d and R^+ endowed with the Riemannian symmetric space metric and the right Haar measure: this is a Lie group of exponential growth. In this paper we define an Hardy space H^1 and a BMO space in this…

We study a factorization of bounded linear maps from an operator space $A$ to its dual space $A^*$. It is shown that $T : A \longrightarrow A^*$ factors through a pair of a column Hilbert spaces $\mathcal{H}_c$ and its dual space if and…

We constructively determine the Pietsch measure of the 2-summing multiplication operator \[\mathcal{M}_u:\ell^{\infty} \rightarrow H^p, \quad (\varphi_I) \mapsto \sum \varphi_Ix_Ih_I. \] Our construction of the Pietsch measure for the…

In this paper, we prove the boundedness of matrix Hausdorff operators and rough Hausdorff operators in the two weighted Herz-type Hardy spaces associated with both power weights and Muckenhoupt weights. By applying the fact that the…