On bilinear Littlewood-Paley square functions.

Lacey, Michael T.. "On bilinear Littlewood-Paley square functions.." Publicacions Matemàtiques 40.2 (1996): 387-396. <http://eudml.org/doc/41268>.

@article{Lacey1996,
abstract = {On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.},
author = {Lacey, Michael T.},
journal = {Publicacions Matemàtiques},
keywords = {Funcional cuadrático; Formas bilineales continuas; Transformada de Fourier; Soporte compacto; Operador bilineal; Funciones de Littlewood-Paley; Desigualdades; Espacios de Hilbert; Puntos singulares; bilinear Hilbert transform; bilinear Littlewood-Paley square functions; Fourier transform},
language = {eng},
number = {2},
pages = {387-396},
title = {On bilinear Littlewood-Paley square functions.},
url = {http://eudml.org/doc/41268},
volume = {40},
year = {1996},
}

TY - JOUR
AU - Lacey, Michael T.
TI - On bilinear Littlewood-Paley square functions.
JO - Publicacions Matemàtiques
PY - 1996
VL - 40
IS - 2
SP - 387
EP - 396
AB - On the real line, let the Fourier transform of kn be k'n(ξ) = k'(ξ-n) where k'(ξ) is a smooth compactly supported function. Consider the bilinear operators Sn(f, g)(x) = ∫ f(x+y)g(x-y)kn(y) dy. If 2 ≤ p, q ≤ ∞, with 1/p + 1/q = 1/2, I prove thatΣ∞n=-∞ ||Sn(f,g)||22 ≤ C2||f||p2||g||q2.The constant C depends only upon k.
LA - eng
KW - Funcional cuadrático; Formas bilineales continuas; Transformada de Fourier; Soporte compacto; Operador bilineal; Funciones de Littlewood-Paley; Desigualdades; Espacios de Hilbert; Puntos singulares; bilinear Hilbert transform; bilinear Littlewood-Paley square functions; Fourier transform
UR - http://eudml.org/doc/41268
ER -