Abstract
We provide some remarks concerning a bilinear square function formed by products of Littlewood–Paley operators over arbitrary intervals. For 1 < p 1, p 2 < ∞ with 1∕p = 1∕p 1 + 1∕p 2, we show that this square function is bounded from \(L^{p_{1}}(\mathbf{R}) \times L^{p_{2}}(\mathbf{R})\) to L p(R) when p > 2∕3 and unbounded when p < 2∕3.
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The author would like to acknowledge the Simons Foundation.
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Grafakos, L. (2016). A Remark on Bilinear Square Functions. In: Pereyra, M., Marcantognini, S., Stokolos, A., Urbina, W. (eds) Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1). Association for Women in Mathematics Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-30961-3_9
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DOI: https://doi.org/10.1007/978-3-319-30961-3_9
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