Boundedness of Calderon-Zygmund singular integral operators from l1(Lp) into weak - l1(Lp)

Boundedness of Singular Integral Operators On

Eleonor Harboure Beairiz Viviani Presentado pOl" Carlos Segovia Abstract: We study the boundedness of singular integral operators on Orlicz-Hardy spaces H w , in the setting of spaces of homogeneous type. As an application of this result, we obtain a characterization of HwIRn in terms of the Riesz Transforms. § 1. NOTATION AND DEFINITIONS Let X be a set. A function d : X x X -+ IR+ U {OJ shall ...

A Note on Calderón-zygmund Singular Integral Convolution Operators

Convolution Calderón-Zygmund singular integral operators with rough kernels

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

Singular Integrals: The Roles of Calderon and Zygmund

1130 NOTICES OF THE AMS VOLUME 45, NUMBER 9 T he subject matter of this essay is Alberto Calderón’s pivotal role in the creation of the modern theory of singular integrals. In that great enterprise Calderón had the good fortune of working with Antoni Zygmund, who was at first his teacher and mentor and later his collaborator. For that reason any account of that theory has to be in part the stor...

Wavelet Decomposition of Calderon - Zygmund Operators on Function Spaces

We make use of the Beylkin-Coifman-Rokhlin wavelet decomposition algorithm on the CalderonZygmund kernel to obtain some fine estimates on the operator and prove the T(\) theorem on Besov and Triebel-Lizorkin spaces. This extends previous results of Frazier et at., and Han and Hofmann. 2000 Mathematics subject classification: primary 42B20, 46B30.