On bilinear Littlewood-Paley square functions.
Lacey, Michael T.
Publicacions Matemàtiques, Tome 40 (1996), p. 387-396 / Harvested from Biblioteca Digital de Matemáticas
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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 that

Σ∞ n=-∞ ||Sn(f,g)||2 2 ≤ C2||f||p 2||g||q 2.

The constant C depends only upon k.

Publié le : 1996-01-01
DMLE-ID : 3805 
@article{urn:eudml:doc:41268,
     title = {On bilinear Littlewood-Paley square functions.},
     journal = {Publicacions Matem\`atiques},
     volume = {40},
     year = {1996},
     pages = {387-396},
     mrnumber = {MR1425626},
     zbl = {0869.42005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41268}
}

Lacey, Michael T. On bilinear Littlewood-Paley square functions.. Publicacions Matemàtiques, Tome 40 (1996) pp. 387-396. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41268/