On some singular integral operatorsclose to the Hilbert transform

Godoy, T., Saal, L., and Urciuolo, M.. "On some singular integral operatorsclose to the Hilbert transform." Colloquium Mathematicae 72.1 (1997): 9-17. <http://eudml.org/doc/210458>.

@article{Godoy1997,
abstract = {Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^p(ℝ)$-boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_m f(x) = p.v. \int k(x-y) m(x+y) f(y)dy$ where $k(x) = \sum _\{j ∈ ℤ\} 2^j φ _j (2^j x)$ for a family of functions $\{φ_j\}_\{j∈ℤ\}$ satisfying conditions (1.1)-(1.3) given below.},
author = {Godoy, T., Saal, L., Urciuolo, M.},
journal = {Colloquium Mathematicae},
keywords = {singular integral operators; Hilbert transform},
language = {eng},
number = {1},
pages = {9-17},
title = {On some singular integral operatorsclose to the Hilbert transform},
url = {http://eudml.org/doc/210458},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Godoy, T.
AU - Saal, L.
AU - Urciuolo, M.
TI - On some singular integral operatorsclose to the Hilbert transform
JO - Colloquium Mathematicae
PY - 1997
VL - 72
IS - 1
SP - 9
EP - 17
AB - Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^p(ℝ)$-boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_m f(x) = p.v. \int k(x-y) m(x+y) f(y)dy$ where $k(x) = \sum _{j ∈ ℤ} 2^j φ _j (2^j x)$ for a family of functions ${φ_j}_{j∈ℤ}$ satisfying conditions (1.1)-(1.3) given below.
LA - eng
KW - singular integral operators; Hilbert transform
UR - http://eudml.org/doc/210458
ER -