On the Cesàro-Perron integral

The Strong Perron Integral

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

THE STRONG PERRON INTEGRAL IN THE n-DIMENSIONAL SPACE R

In this paper, we introduce the SP -integral and the SPα-integral defined on an interval in the n-dimensional Euclidean space Rn. We also investigate the relationship between these two integrals.

On generalized absolute Cesàro summability

In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.

Summability of the l-1 Cesàro means of an integral transformation connected to a Riesz potential

Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro (C, δ) means for two-variable Jacobi polynomials on the parabolic biangle B = {(x1, x2) ∈ R2 : 0 ≤ x1 ≤ x2 ≤ 1}. Using the product formula derived by Koornwinder & Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C, δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ > ...