Nonabsolutely convergent Poisson integrals
نویسنده
چکیده
If a function f has finite Henstock integral on the boundary of the unit disk of R 2 then its Poisson integral exists for |z| < 1 and is o((1 − |z|) −1) as |z| → 1 −. It is shown that this is the best possible uniform pointwise estimate. For an L 1 measure the best estimate is O((1 − |z|) −1). In this paper we consider estimates of Poisson integrals on the unit circle with respect to Alexiewicz and L p norms. Define the open disk in R 2 as D := {re iθ | 0 ≤ r < 1, −π < θ ≤ π} and let the unit circle T be its boundary.
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