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Weak type estimates for Cesàro sums of Jacobi polynomial series

About this Title

Sagun Chanillo and Benjamin Muckenhoupt

Publication: Memoirs of the American Mathematical Society
Publication Year 1993: Volume 102, Number 487
ISBNs: 978-0-8218-2548-8 (print); 978-1-4704-0064-4 (online)
MathSciNet review: 1132609
MSC: Primary 42C10; Secondary 33C45, 40G05, 42A24, 42A50

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Table of Contents


  • 1. Introduction
  • 2. Facts and definitions
  • 3. An absolute value estimate for $3(1-y) \leq 2(1-x)$
  • 4. A basic estimate for $3(1-y) \leq 2(1-x)$
  • 5. A kernel estimate for $3(1-y) \leq 2(1-x)$ and $-1 \leq \theta \leq 0$
  • 6. A reduction lemma
  • 7. A kernel estimate for $3(1-y) \leq 2(1-x)$ and $\theta \geq -$1
  • 8. A Cesaro kernel estimate for $t \leq s/2$
  • 9. A basic estimate for separated arguments
  • 10. A reduction lemma for separated arguments
  • 11. A kernel estimate for separated arguments
  • 12. Cesaro kernel estimate for $t \leq s - b$
  • 13. Cesaro kernel estimate for $s$ near $t$
  • 14. Kernel estimates
  • 15. A weak type lemma
  • 16. Lemmas for the upper critical value
  • 17. Proofs of theorems (1.1)–(1.3)
  • 18. Norm estimates for $p$ not between the critical values
  • 19. A polynomial norm inequality
  • 20. A lower bound for a norm of the kernel
  • 21. Some limitations of the basic results
  • 22. Growth of Cesaro means
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