Weak-type (1,1) bounds for a class of
operators with discrete kernel

DUVÁN CARDONA^*,

Universidad del Valle, Department of Mathematics, A.A. 25360, Cali, Colombia.

Abstract. In this paper we investigate the weak continuity of a certain class of operators with kernel defined on ℤ × ℤ. We prove some results on the weak boundedness of discrete analogues of Calderón-Zygmund operators. The considered operators arise from the study of discrete pseudo-differential operators and discrete analogues of singular integral operators.

Keywords: L^p spaces, discrete operator, pseudo-differential operator, Calderón-Zygmund decomposition.
MSC2010: 47B34, 47G10, 28A25.

Cotas del tipo débil (1,1) para una clase de operadores
con núcleo discreto

Resumen. En este trabajo se investigará el tipo débil (1,1) de una cierta clase de operadores con núcleo definido sobre ℤ × ℤ. Se estudiará la continuidad débil de operadores que son análogos discretos de los ahora conocidos, operadores singulares integrales de Calderón-Zygmund. Los operadores considerados surgen desde el estudio de operadores pseudo diferenciales de tipo discreto y versiones discretas de integrales singulares.

Palabras clave: Espacios L^p, operador discreto, operador pseudo diferencial, descomposición de Calderón-Zygmund.

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^*E-mail: duvanc306@gmail.com.
Received: 09 September 2014, Accepted: 10 March 2015.
To cite this article: D. Cardona, Weak-type (1,1) bounds for a class of operators with discrete kernel, Rev. Integr. Temas Mat. 33 (2015), no. 1, 51-60.