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A Note on Interpolation in Hardy Spaces

  • Francesc Tugores
  • Laia Tugores
Original Paper
  • 7 Downloads

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 \(p=2\).

Keywords

Hardy space Carleson measure Uniformly separated sequence Interpolating sequence 

Mathematics Subject Classification

Primary 30E05 Secondary 30H10 30H05 

Notes

Acknowledgements

We thank the referee for very valuable comments.

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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VigoOurenseSpain
  2. 2.Colegio María Auxiliadora, SalesianosOurenseSpain

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