E. Talvila

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20012004

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math.CA2004

Estimates of the remainder in Taylor's theorem using the Henstock--Kurzweil integral

Erik Talvila

When a real-valued function of one variable is approximated by its $n^{t h}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$ -norms in case…

math.CA2004

Estimates of Henstock--Kurzweil Poisson integrals

Erik Talvila

If $f$ is a real-valued function on $[- π, π]$ that is Henstock--Kurzweil integrable, let $u_{r} (θ)$ be its Poisson integral. It is shown that $∥ u_{r} ∥_{p} = o (1/ (1 - r))$ as $r \to 1$ and th…