In the paper by Sedleckiĭ, A. M.

*An equivalent definition of the spaces in the half-plane, and some applications.* (Russian)

Mat. Sb. (N.S.) 96(138) (1975), 75–82, 167, the following is proved: given an analytic function on the upper-half plane consider the following two quantities for :

and

Then

for some constants .

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