Abstract
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 \(p=2\).
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We thank the referee for very valuable comments.
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Communicated by Ali Abkar.
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Tugores, F., Tugores, L. A Note on Interpolation in Hardy Spaces. Bull. Iran. Math. Soc. 45, 607–615 (2019). https://doi.org/10.1007/s41980-018-0152-4
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DOI: https://doi.org/10.1007/s41980-018-0152-4