A Note on Interpolation in Hardy Spaces
This note deals with an interpolation problem in the disk. We impose that the interpolation be performed exclusively by the first derivative of a function in a certain Hardy space \(H^p\). When \(1<p<\infty \), we characterize the corresponding interpolating sequences as the separated ones that also verify a condition for all functions in \(H^q\) (p and q are conjugate exponents). We also prove that the interpolating sequences for \(p=1\) are the same as for \(p=2\).
KeywordsHardy space Carleson measure Uniformly separated sequence Interpolating sequence
Mathematics Subject ClassificationPrimary 30E05 Secondary 30H10 30H05
We thank the referee for very valuable comments.