On a discrete bilinear singular operator期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On a discrete bilinear singular operator

Authors:	Dong Dong

Affiliation:	Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green Street, Urbana, IL 61801, USA

Abstract:	We prove that for a large class of functions P and Q, the discrete bilinear operator $T_{P, Q} (f, g) (n) = \sum_{m \in Z ? {0}} f (n ? P (m)) g (n ? Q (m)) \frac{1}{m}$ is bounded from $l^{2} \times l^{2}$ into $l^{1 + ?, \infty}$ for any $? \in (0, 1]$ .

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