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

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Appendix A

Hardy spaces

This appendix is intended as a brief summary of the basic elements of the theory of Hardy spaces. For the most part, we state results without proof. Unless explicit references are given, proofs can be found in [104, Chapter 17], which provides a succinct introduction to the subject. The reader seeking more details is referred to the specialized texts on Hardy spaces [40, 50, 66, 77].

A.1 Hardy spaces

Definition A.1.1   For 0 < p < ∞, the Hardy space Hp is defined by

image

Also we define

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Finally, the Nevanlinna class is defined ...

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