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A Primer on the Dirichlet Space by Thomas Ransford, Javad Mashreghi, Karim Kellay, Omar El-Fallah

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7

Harmonically weighted Dirichlet spaces

In §1.6, we introduced the notion of a weighted Dirichlet integral. Given a measurable function image we defined

image

In this chapter we are going to examine in some detail a special class of weights, namely those w that are harmonic functions on image. There are (at least) two reasons why these particular weights are important.

Firstly, a general harmonic weight w can be synthesized as an average of extreme harmonic weights, ...

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