Memoirs of the American Mathematical Society 1993; 90 pp; softcover Volume: 102 ISBN10: 0821825488 ISBN13: 9780821825488 List Price: US$34 Individual Members: US$20.40 Institutional Members: US$27.20 Order Code: MEMO/102/487
 This work completely characterizes the behavior of Cesaro means of any order of the Jacobi polynomials. In particular, pointwise estimates are derived for the Cesaro mean kernel. Complete answers are given for the convergence almost everywhere of partial sums of Cesaro means of functions belonging to the critical \(L^p\) spaces. This characterization is deduced from weak type estimates for the maximal partial sum operator. The methods used are fairly general and should apply to other series of special functions. Readership Research mathematicians. Table of Contents  Facts and definitions
 An absolute value estimate for \(3(1y)\leq 2(1x)\)
 A basic estimate for \(3(1y)\leq 2(1x)\)
 A kernel estimate for \(3(1y)\leq 2(1x)\) and \(1\leq \theta \leq 0\)
 A reduction lemma
 A kernel estimate for \(3(1y)\leq 2(1x)\) and \(\theta \geq 1\)
 A Cesaro kernel estimate for \(t\leq s/2\)
 A basic estimate for separated arguments
 A reduction lemma for separated arguments
 A kernel estimate for separated arguments
 Cesaro kernel estimate for \(t\leq sb\)
 Cesaro kernel estimate for \(s\) near \(t\)
 Kernel estimates
 A weak type lemma
 Lemmas for the upper critical value
 Proofs of theorems (1.1)(1.3)
 Norm estimates for \(p\) not between the critical values
 A polynomial norm inequality
 A lower bound for a norm of the kernel
 Some limitations of the basic result
 Growth of Cesaro means
