Inversion theorem for bilinear Hilbert transform
نویسندگان
چکیده
منابع مشابه
Inversion Theorem for Bilinear Hilbert Transform
where f ∈ L2(R) and g ∈ L∞(R), respectively f ∈ Lp1(R) and g ∈ Lp2(R), 1 < p1, p2 <∞. Their main result is the affirmative answer on the Calderon conjecture, first for p1 = 2, p2 = ∞ ([5]), then for p1, p2 ∈ (1,∞). Let 2/3 < p = p1p2 p1+p2 or p1 = 2, p2 = ∞ and p = 2. Then their main result is ||Hα(f, a)||Lp ≤ C||f ||Lp1 ||a||Lp2 , f ∈ L p1, a ∈ Lp2, where C > 0 depends on α, p1, p2. We refer t...
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For the bilinear Hilbert transform given by: H fg(x) = p.v.integral f(x - y)g(x + y) dyy, we announce the inequality parallel H fg parallel (p(3) ) </= K(p(1) ) (,p(2) ) parallel f parallel (p(1) ) parallel g parallel (p(2) ), provided 2 < p(1), p(2) < infinity, 1/p(3) = 1/p(1) + 1/p(2) and 1 < p(3) < 2.
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ژورنال
عنوان ژورنال: Integral Transforms and Special Functions
سال: 2008
ISSN: 1065-2469,1476-8291
DOI: 10.1080/10652460701855948