On Calderón's conjecture

Michael Lacey and Christoph Thiele

Review from Zentralblatt MATH:

This paper is in continuation of authors' earlier paper [Ann. Math., II. Ser. 146, No. 3, 693-724 (1997; Zbl 0914.46034)] in which they discussed bilinear operators of the form $$H_\alpha(f_1,f_2)(x):= \text{p.v. }\int f_1(x- t) f_2(x+\alpha t) dt/t\tag{$*$}$$ which are originally defined for $f_1$ and $f_2$ in the Schwartz class $S(\bbfR)$. The authors investigate whether estimates of the form $$\|H_\alpha(f_1, f_2)\|_p\le C_{\alpha,p_1,p_2}\|f_1\|_{p_1}\|f_2\|_{p_2}\tag{$

Reviewed by Ram Kishore Saxena

Keywords: singular integrals; bilinear operators; Marcinkiewicz interpolation; maximal functions; partial order; Calderón-Zygmund theory; orthogonality

Classification (MSC2000): 42B20 44A15 42A50 46F12

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