Poisson integrals and singular weights

Weights for maximal functions and singular integrals

These notes are a guide for the course to be taught at the NCTS 2005 Summer School on Harmonic Analysis in Taiwan. They contain a description of results and sometimes short indications about the proofs. Moreover, each section contains a list of references. For an introduction to the subject it is better to go to the books mentioned in the bibliography at the end of the notes: each one of them i...

Singular Integrals

In this paper I will a t tempt to describe the subject as it has developed in the last fifteen years, outlining the methods by which its problems have been approached and discussing its connections with other branches of Analysis. I t will perhaps be best to start by considering certain classical situations which lead naturally to singular integrals and which contain the seeds of some of the me...

Evaluating Singular and Nearly Singular Integrals Numerically

Nonabsolutely convergent Poisson integrals

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...

Multi-parameter singular integrals