Blasco, Oscar Notes on the spaces of bilinear multipliers. (English) Zbl 1209.42007 Rev. Unión Mat. Argent. 50, No. 2, 23-37 (2009). A bounded operator from \(L^{P_1}(\mathbb{R}) \times L^{P_2}(\mathbb{R}) \rightarrow L^{P_3}(\mathbb{R})\) of the form \[ \displaystyle B (f,g) (x) = \int\limits_{\mathbb{R}^n}\int\limits_{\mathbb{R}^n}\hat{f}(\xi)\hat{g}(\eta) m(\xi, \eta) e^{2 \pi \iota (\xi + \eta, x)} d \xi d \eta, \] where \(m\) is a locally integrable function, is called a bilinear multiplier on \(\mathbb{R}\) of type \((p_1, p_2, p_3)\). In this well written paper, the author studies basic properties of bilinear multipliers and the space of bilinear multipliers of type \((p_1, p_2, p_3)\). About half the paper is devoted to the special class of multipliers of the form \(m(\xi, \eta)= M(\xi - \eta)\) for a real-valued function \(M\). This class includes the important examples of the bilinear fractional integral and the bilinear Hilbert transform. Reviewer: Kathryn Hare (Waterloo) Cited in 6 Documents MSC: 42B15 Multipliers for harmonic analysis in several variables 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Keywords:bilinear multipliers; bilinear convolution-type operators; bilinear multiplier spaces PDFBibTeX XMLCite \textit{O. Blasco}, Rev. Unión Mat. Argent. 50, No. 2, 23--37 (2009; Zbl 1209.42007) Full Text: arXiv