Abstract
We consider the action of the Hilbert matrix operator, H; on the Hardy space H 1 , weighted Hardy spaces H p fi (fi ‚ 0); Bergman spaces with logarithmic weights, etc. In particular, we extend Diamantopoulos-Siskakis result by proving that H maps H p fi into H p if and only if fi+1=p 3: Similarly, the Bloch space with logarithmic weight is mapped by H into the ordinary Bloch space.
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