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Paper   IPM / M / 17679
School of Mathematics
  Title:   Pointwise domination and weak $L^{1}$ boundedness of Littlewood-Paley operators via sparse operators
  Author(s):  Mehdi Hormozi
  Status:   In Proceedings
  Proceeding: Trends in Mathematics
  Year:  2024
  Pages:   49-56
  Editor:  Ruzhansky, M., Van Bockstal, K.
  Supported by:  IPM
This contribution is based on joint work with Hormozi et al. (J. Fourier Anal. Appl. 29:49, 2023). We simplify and shorten the proofs of the main results of Shi et al. (J. Math. Pures Appl. 101:394�¢??413, 2014) significantly. In particular, the new proof for Shi et al. (J. Math. Pures Appl. 101:394�¢??413, 2014; Theorem 1.1) is quite short and, unlike the original proof, does not rely on the properties of the �¢??Marcinkiewicz function�¢?�. This allows us to get a precise linear dependence on Dini constants with a subsequent application to Littlewood�¢??Paley operators by the well-known techniques.

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