On some singular integral operatorsclose to the Hilbert transform
Volume 72 / 1997
Colloquium Mathematicum 72 (1997), 9-17
DOI: 10.4064/cm-72-1-9-17
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.
