Paper's Title:

A Note on Schur's Lemma in Banach Function Spaces

Author(s):

R. E. Castillo, H. Rafeiro and E. M. Rojas

Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: recastillo@unal.edu.co
 
United Arab Emirates University,
Department of Mathematical Sciences, Al Ain,
United Arab Emirates.
E-mail: rafeiro@uaeu.ac.ae

Universidad Nacional de Colombia,
Departamento de Matematicas, Bogota,
Colombia.
E-mail: emrojass@unal.edu.co

Abstract:

In this small note, in a self contained presentation, we show the validity of Schur's type lemma in the framework of Banach function spaces.

Paper's Title:

Bilinear Regular Operators on Quasi-Normed Functional Spaces

Author(s):

D. L. Fernandez and E. B. Silva

Universidade Estadual de Campinas - Unicamp
Instituto de Matematica
Campinas - SP
Brazil.
E-mail: dicesar@ime.unicamp.br

Universidade Estadual de Maringa--UEM
Departamento de Matematica
Av.~Colombo 5790
Maringa - PR
Brazil.
E-mail: ebsilva@uem.br

Abstract:

Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators and their adjoints in normed functional spaces are also studied.

Paper's Title:

On the Boundedness of the Discrete Hilbert Transform: An Elementary Proof

Author(s):

R. E. Castillo and H. C. Chaparro

Department of Mathematics,
Universidad Nacional de Colombia,
Bogota,
Colombia..
E-mail: recastillo@unal.edu.co

Program of Mathematics,
Universidad de Cartagena,
Cartagena de Indias,
Colombia.
E-mail: hchaparrog@unicartagena.edu.co

Abstract:

In this short note, we present an elementary proof of the boundedness of the discrete Hilbert transform on l_p(Z)$ spaces for 1 < p < ∞. Our approach relies solely on Hölder's inequality, avoiding more sophisticated tools from harmonic analysis. This offers a simplified and accessible pathway to understanding a classical result in operator theory.

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