On Calderón ’ S Conjecture 477
نویسندگان
چکیده
(2) ‖Hα(f1, f2)‖p ≤ Cα,p1,p2‖f1‖p1‖f2‖p2 with constants Cα,p1,p2 depending only on α, p1, p2 and p := p1p2 p1+p2 hold. The first result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular, the case p1 = 2, p2 = ∞ is solved to the affirmative. This was originally considered to be the most natural case and is known as Calderón’s conjecture [3]. We prove the following theorem: Theorem 1. Let α ∈ R \ {0,−1} and
منابع مشابه
ON CALDERÓN ’ S CONJECTURE 477 Next
(2) ‖Hα(f1, f2)‖p ≤ Cα,p1,p2‖f1‖p1‖f2‖p2 with constants Cα,p1,p2 depending only on α, p1, p2 and p := p1p2 p1+p2 hold. The first result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular, the case p1 = 2, p2 = ∞ is solved to the affirmative. This was originally considered to be the most natural ...
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