×

zbMATH — the first resource for mathematics

Carleson conditions for the Poisson integral. (English) Zbl 0748.42009
The authors study the weighted norm inequality \[ \left(\iint_{\mathbb{R}_ +^{n+1}}| Pf(x,t)|^ qw(x,t)dx dt\right)^{1/q}\leq c\left(\int_{\mathbb{R}^ n}| f(x)|^ pv(x)dx\right)^{1/p} \] with a constant \(c\) independent of \(f\), where \(Pf\) is the Poisson integral of \(f\) and \(1<p\leq q<\infty\). They obtain necessary and sufficient conditions for this inequality to be true. These conditions simplify the previous ones obtained by the same authors. The case \(p=q\) which brings additional difficulties is considered separately.

MSC:
42B25 Maximal functions, Littlewood-Paley theory
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
PDF BibTeX XML Cite
Full Text: DOI