Geodesic
On approach regions for the conjugate Poisson integral and singular integrals
Studia Mathematica, Tome 120 (1996) no. 2, pp. 169-182

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let ũ denote the conjugate Poisson integral of a function $f ∈ L^{p}(ℝ)$. We give conditions on a region Ω so that $lim_{(v,ε)→(0,0)}_{(v,ε)∈Ω} ũ(x+v,ε) = Hf(x)$, the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that $sup_{(v,r)∈Ω} |ʃ_{|t|>r} k(x+v-t)f(t)dt|$ is a bounded operator on $L^p$, 1 p ∞, and is weak (1,1).
DOI : 10.4064/sm-120-2-169-182
Keywords: cone condition, conjugate Poisson integral, singular integrals, ergodic Hilbert transform

S. Ferrando 1 ;  1 ;  1

1 
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S. Ferrando;  ;  . On approach regions for the conjugate Poisson integral and singular integrals. Studia Mathematica, Tome 120 (1996) no. 2, pp. 169-182. doi: 10.4064/sm-120-2-169-182

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