Abstract
We present an explicit construction of examples showing that the estimate \(\Vert T^\epsilon \Vert _{L^1(w)\rightarrow L^{1,\infty }(w)}\)\(\lesssim [w]_{A_1}\log (1+[w]_{A_1})\) for Haar multipliers is sharp in terms of the characteristic \([w]_{A_1}\).
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The research was supported by Narodowe Centrum Nauki (Poland) Grant DEC-2014/14/E/ST1/00532.
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Osękowski, A. Explicit counterexamples to the weak Muckenhoupt–Wheeden conjecture. Math. Z. 298, 1727–1734 (2021). https://doi.org/10.1007/s00209-020-02656-9
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DOI: https://doi.org/10.1007/s00209-020-02656-9