Bourgain’s analytic projection revisited

Kislyakov, S.

doi:10.1090/S0002-9939-98-04502-X

Bourgain’s analytic projection revisited
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by S. V. Kislyakov

Proc. Amer. Math. Soc. 126 (1998), 3307-3314

DOI: https://doi.org/10.1090/S0002-9939-98-04502-X

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Abstract:

For a positive function $w$ on the unit circle with $\log w\in L^1$, the following two statements are equivalent: (a) $\log w\in BMO$; (b) there is an operator $Q$ projecting $L^p(w)$ onto $H^p(w)$ for all $1<p<\infty$ at once and having weak type (1,1) with respect to $w$.

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