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On Calderón's conjecture | | Michael Lacey
; Christoph Thiele
; | | Date: |
1 Mar 1999 | | Journal: | Ann. of Math. (2) 149 (1999), no. 2, 475-496 | | Subject: | Classical Analysis and ODEs; Functional Analysis | math.CA math.FA | | Abstract: | This paper is a successor of cite{laceyt}. In that paper we considered bilinear operators of the form H_alpha(f_1,f_2)(x) = p.v. int f_1(x-t) f_2(x + alpha t)/t dt, which are originally defined for f_1, f_2 in the Schwartz class S(R). The natural question is whether estimates of the form H_alpha(f_1,f_2)|_p <= C_{alpha,p_1,p_2} |f_1|_{p_1} |f_2|_{p_2} with constants C_{alpha,p_1,p_2} depending only on alpha,p_1,p_2 and p = p_1p_2/(p_1+p_2) hold. The purpose of the current paper is to extend the range of exponents p_1 and p_2 for which the estimate is known. In particular, the case p_1=2, p_2=infty is solved to the affirmative. This was originally considered to be the most natural case and is known as Calderón’s conjecture. | | Source: | arXiv, math.CA/9903203 | | Services: | Forum | Review | PDF | Favorites | |
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