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The Boundedness of Calderón-Zygmund Operators on Wavelet Spaces

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Part of the Lecture Notes in Mathematics book series (LNM, volume 1966)

We first define test functions and wavelet spaces on spaces of homogeneous type. Then we prove the main result of this chapter, namely that Calderón-Zygmund operators whose kernels satisfy an additional smoothness condition are bounded on wavelet spaces. This result will be a crucial tool to provide wavelet expansions of functions and distributions on spaces of homogeneous type in the next chapter.

We first introduce test functions on spaces of homogeneous type.

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© Springer-Verlag Berlin Heidelberg 2009

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