# Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series

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*Sagun Chanillo; Benjamin Muckenhoupt*

#### Table of Contents

# Table of Contents

## Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series

- Table of Contents vii8 free
- § 1. Introduction 110 free
- § 2. Facts and definitions 615 free
- § 3. An absolute value estimate for 3(1…y) ≤ 2(1…x) 1221
- § 4. A basic estimate for 3(1…y) ≤ 2(1…x) 1524
- § 5. A kernel estimate for 3(1…y) ≤ 2(1…x) and …1 ≤ θ ≤ 0 2029
- § 6. A reduction lemma 2332
- § 7. A kernel estimate for 3(1…y) ≤ 2(1…x) and 0 ≥ …1 2837
- § 8. A Cesaro kernel estimate for t ≤ s/2 3140
- § 9. A basic estimate for separated arguments 3544
- §10. A reduction lemma for separated arguments 3746
- §11. A kernel estimate for separated arguments 3948
- §12. Cesaro kernel estimate for t ≤ s … b 4049
- §13. Cesaro kernel estimate for s near t 4251
- §14. Kernel estimates 4655
- §15. A weak type lemma 5160
- §16. Lemmas for the upper critical value 6271
- §17. Proofs of theorems (1.1) – (1.3) 7281
- §18. Norm estimates for p not between the critical values 7483
- §19. A polynomial norm inequality 7887
- §20. A lower bound for a norm of the kernel 8190
- §21. Some limitations of the basic results 8493
- §22. Growth of Cesaro means 8897
- §23. References 9099