Boundness of Cesàro Means Operators

Boundedness of Projection Operators and Cesàro Means in Weighted L Space on the Unit Sphere

For the weight function Qd+1 i=1 |xi| 2κi on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the convergence of the Cesàro (C, δ) means in the weighted L space for δ below the critical index. Similar results are also proved for corresponding weight functions on the unit ball and on the simplex.

Estimate of the Approximation of Periodic Functions by Negative Cesàro Means

Products of Cesàro Convergent Sequences with Applications to Convex Solid Sets and Integral Operators

Let 0 ≤ an, bn, cn such that an = bncn. If a = limn→∞ an, and {bn} and {cn} Cesàro converge to b, respectively c, then a ≤ bc. This implies that if in addition {bn} and {cn} are similarly ordered, then a = bc. As applications we prove that the pointwise product of two convex solid sets closed in measure is again closed in measure and a factorization result for kernels of regular integral operat...

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for δ below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order δ.

On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series

The behavior of generalized Cesàro (C, αn)-means (αn ∈ (−1, 0), n = 1, 2, . . . ) of conjugate trigonometric Fourier series of H classes in the space of continuous functions is studied. 2000 Mathematics Subject Classification: 42A50.