G. Curbera

activity

20152026

most citedInversion and extension of the finite Hilbert transform on (-1,1)

7 citations · 13 across the 13 of their papers we have counts for

collaborators

16 papers

math.FA2026

The finite Hilbert transform acting on $L^{\infty}$

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

The action of the finite Hilbert transform defined on $L^{\infty} (- 1, 1)$ and taking its values in the Zygmund space $L_{exp} (- 1, 1)$ is studied in detail. This is a recip…

math.FA2024

Measure theoretic aspects of the finite Hilbert transform

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

The finite Hilbert transform $T$ , when acting in the classical Zygmund space $\logl$ (over $(- 1, 1)$ ), was intensively studied in \cite{curbera-okada-ricker-log}. In this note an in…

math.FA2023

A note on extreme points of the unit of Hardy-Lorentz spaces

Javier Carrillo-Alanís, Guillermo P. Curbera

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

math.FA2023

The finite Hilbert transform on $(- 1, 1)$

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

We present a detailed survey of recent developments in the study of the finite Hilbert transform and its corresponding inversion problem in rearrangement invariant spaces on $(-1,1…

math.FA2023

Extension and Integral Representation of the finite Hilbert Transform In Rearrangement Invariant Spaces

G. P. Curbera, S. Okada, W. J. Ricker

The finite Hilbert transform $T$ is a classical (singular) kernel operator which is continuous in every rearrangement invariant space $X$ over $(- 1, 1)$ having non-trivial Boyd indi…

math.FA2023

The Cesàro space of Dirichlet series and its multiplier algebra

Jorge Bueno-Contreras, Guillermo P. Curbera, Olvido Delgado

We consider the space $H (ce s_{p})$ of all Dirichlet series whose coefficients belong to the Cesàro sequence space $ce s_{p}$ , consisting of all complex sequences whose absolut…

math.FA2023

Fine spectra and compactness of generalized Cesàro operators in Banach lattices in $C^{N_{0}}$

Guillermo P. Curbera, Werner J. Ricker

The generalized Cesàro operators $C_{t}$ , for $t \in [0, 1)$ , introduced in the 1980's by Rhaly, are natural analogues of the classical Cesàro averaging operator $\mathcal{C}_…

math.FA2023

Convolution in dual Cesàro sequence spaces

Guillermo P. Curbera, Werner J. Ricker

We investigate convolution operators in the sequence spaces $d_{p}$ , for $1 \leq p < \infty$ . These spaces, for $p > 1$ , arise as dual spaces of the \ces sequence spaces $ce s_{p}$ thoroughly…

math.FA2022

The finite Hilbert transform acting in the Zygmund space LlogL

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

The finite Hilbert transform T is a singular integral operator which maps the Zygmund space $L l o g L := L l o g L (- 1, 1)$ continuously into $L^{1} := L^{1} (- 1, 1)$ . By extending the Parseval and P…

math.FA2020

Rosenthal's space revisited

Sergey V. Astashkin, Guillermo P. Curbera

Let $E$ be a rearrangement invariant (r.i.) function space on $[0, 1]$ , and let $Z_{E}$ consist of all measurable functions $f$ on $(0, \infty)$ such that $f^{*} χ_{[0, 1]} \in E$ and $f^*χ…

math.FA2019

Fine spectra of the finite Hilbert transform in function spaces

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

We investigate the spectrum and fine spectra of the finite Hilbert transform acting on rearrangement invariant spaces over $(- 1, 1)$ with non-trivial Boyd indices, thereby extending…

math.FA2019

Non-extendability of the finite Hilbert transform

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

It is proved that the finite Hilbert transform $T : X \to X$ , which acts continuously on every rearrangement invariant space $X$ on $(- 1, 1)$ having non-trivial Boyd indices, is…

math.FA2019★ 7 cited

Inversion and extension of the finite Hilbert transform on (-1,1)

Guillermo P. Curbera, Susumu Okada, Werner J. Ricker

The principle of optimizing inequalities, or their equivalent operator theoretic formulation, is well established in analysis. For an operator, this corresponds to extending its ac…

math.CA2016★ 5 cited

Invariant properties for Wronskian type determinants of classical and classical discrete orthogonal polynomials under an involution of sets of positive integers

Guillermo P. Curbera, Antonio J. Duran

Given a finite set $F = {f_{1}, \dots, f_{k}}$ of nonnegative integers (written in increasing size) and a classical discrete family $(p_{n})_{n}$ of orthogonal polynomials (Charlier, Meixn…

math.FA2015

The weak Banach-Saks property for function spaces

Guillermo P. Curbera, Werner J. Ricker

We establish the weak Banach-Saks property for function spaces arising as the optimal domain of an operator.

math.FA2015★ 1 cited

Abstract Cesàro spaces: Integral representations

Guillermo P. Curbera, Werner J. Ricker

The Cesàro function spaces $C e s_{p} = [C, L^{p}]$ , $1 \leq p \leq \infty$ , have received renewed attention in recent years. Many properties of $[C, L^{p}]$ are known. Less is known about $[C, X]$ …

The finite Hilbert transform acting on L∞

Measure theoretic aspects of the finite Hilbert transform

A note on extreme points of the unit of Hardy-Lorentz spaces

The finite Hilbert transform on (−1,1)

Extension and Integral Representation of the finite Hilbert Transform In Rearrangement Invariant Spaces

The Cesàro space of Dirichlet series and its multiplier algebra

Fine spectra and compactness of generalized Cesàro operators in Banach lattices in CN0​

Convolution in dual Cesàro sequence spaces

The finite Hilbert transform acting in the Zygmund space LlogL

Rosenthal's space revisited

Fine spectra of the finite Hilbert transform in function spaces

Non-extendability of the finite Hilbert transform

Inversion and extension of the finite Hilbert transform on (-1,1)

Invariant properties for Wronskian type determinants of classical and classical discrete orthogonal polynomials under an involution of sets of positive integers

The weak Banach-Saks property for function spaces

Abstract Cesàro spaces: Integral representations

The finite Hilbert transform acting on $L^{\infty}$

The finite Hilbert transform on $(- 1, 1)$

Fine spectra and compactness of generalized Cesàro operators in Banach lattices in $C^{N_{0}}$