On approach regions for the conjugate Poisson integral and singular integrals

Ferrando, S., Jones, R., and Reinhold, K.. "On approach regions for the conjugate Poisson integral and singular integrals." Studia Mathematica 120.2 (1996): 169-182. <http://eudml.org/doc/216328>.

@article{Ferrando1996,
abstract = {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).},
author = {Ferrando, S., Jones, R., Reinhold, K.},
journal = {Studia Mathematica},
keywords = {cone condition; conjugate Poisson integral; singular integrals; ergodic Hilbert transform; approach regions; Calderón-Zygmund singular integral; maximal transform; ergodic theory},
language = {eng},
number = {2},
pages = {169-182},
title = {On approach regions for the conjugate Poisson integral and singular integrals},
url = {http://eudml.org/doc/216328},
volume = {120},
year = {1996},
}

TY - JOUR
AU - Ferrando, S.
AU - Jones, R.
AU - Reinhold, K.
TI - On approach regions for the conjugate Poisson integral and singular integrals
JO - Studia Mathematica
PY - 1996
VL - 120
IS - 2
SP - 169
EP - 182
AB - 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).
LA - eng
KW - cone condition; conjugate Poisson integral; singular integrals; ergodic Hilbert transform; approach regions; Calderón-Zygmund singular integral; maximal transform; ergodic theory
UR - http://eudml.org/doc/216328
ER -