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# memo_has_moved_text();Weak type estimates for Cesàro sums of Jacobi polynomial series

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)
DOI: http://dx.doi.org/10.1090/memo/0487
MathSciNet review: 1132609
MSC: Primary 42C10; Secondary 33C45, 40G05, 42A24, 42A50

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Chapters

• 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