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Paper   IPM / M / 16678
School of Mathematics
  Title:   Weak and strong type estimates for the multilinear Littlewood-Paley operators
  Author(s):  Mahdi Hormozi (Joint with M. Cao, G. Ibanez-Fienkorn, I. P. Rivera-Rios, Z. Si, and K. Yabuta)
  Status:   Published
  Journal: Journal of Fourier Analysis and Applications
  Vol.:  27
  Year:  2021
  Pages:   1-42
  Supported by:  IPM
  Abstract:
Let Sα be the multilinear square function defined on the cone with aperture α�?�1. In this paper, we investigate several kinds of weighted norm inequalities for Sα. We first obtain a sharp weighted estimate in terms of aperture α and w�?? �??Ap�?? . By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise A�?? norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley g�??λ function. Some results are new even in the linear case.

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