The Hilbert matrix induces a bounded operator on most Hardy and Bergman spaces, as was shown by Diamantopoulos and Siskakis. We generalize this for any Hankel operator on Hardy spaces by using a result of Hollenbeck and Verbitsky on the Riesz projection and also compute the exact value of the norm of the Hilbert matrix. Using a new technique, we determine the norm of the Hilbert matrix on a wide range of Bergman spaces.
Interpolating sequences for weighted Bergman spaces B p α , 0 < p ≤ ∞, α ≥ −1/p are studied. We show that the natural inclusions between B p α for various p and α are also verified by the corresponding spaces of interpolating sequences. We also give conditions (necessary or sufficient) for the B p α -interpolating sequences. These are similar to the known conditions for the spaces H p and A −α , which in our notation correspond respectively to the particular cases α = −1/p and p = ∞.
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