if f is in $H^{1}$ the Hardy space with integrable norm, and if f is not identically zero, then the zeroes of f (certainly countable in number) satisfy the Blaschke condition.Can any "Blaschke condition" be defined if hardy space is considered on the upper-half plane instead of unit disk. Curious to know if this carries over by the conformal equivalence that maps upper-half plane to unit disk and vice-versa.



Blaschke condition on upper half plane
Blaschke condition in the upper half-plane is $$\sum\left|\Im\frac{1}{z\_k}\right|<\infty.$$
For the proof follow the advice given above, that is prove it yourself, or look in a book.
In addition to the books mentioned above, I recommend Koosis Hardy spaces, or Levin,
Distribution of values of entire functions, or de Branges, Hilbert spaces of entire functions.


