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Transplantation theorems and multiplier theorems for Jacobi series

About this Title

Benjamin Muckenhoupt

Publication: Memoirs of the American Mathematical Society
Publication Year: 1986; Volume 64, Number 356
ISBNs: 978-0-8218-2418-4 (print); 978-1-4704-0772-8 (online)
DOI: https://doi.org/10.1090/memo/0356
MathSciNet review: 858466
MSC: Primary 42C05; Secondary 42A45, 42C15

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Table of Contents

Chapters

  • 1. Introduction
  • 2. Jacobi polynomials
  • 3. A reduction lemma
  • 4. An estimate for separated arguments
  • 5. Kernel estimates for separated arguments
  • 6. An estimate for noncomparable values near 0
  • 7. Kernel estimates for noncomparable values near 0
  • 8. Kernel estimates for comparable values
  • 9. Facts concerning weighted norm inequalities
  • 10. A transplantation lemma without moment conditions
  • 11. A transplantation lemma with moment conditions
  • 12. Proof of the power weight transplantation theorem
  • 13. Multipliers for power weights: a special case
  • 14. Multipliers for power weights
  • 15. Transplantation lemmas with general weights
  • 16. General weight transplantation for $s < \min (\alpha +\gamma +2, \beta +\delta +2)$
  • 17. General weight transplantation for $s \geq \min (\alpha +\gamma +2, \beta +\delta +2)$
  • 18. Moment conditions are essential if $s \geq \min (\alpha +\gamma +2, \beta +\delta +2)$