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.

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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