A proof of the Fefferman-Stein-Strömberg inequality for the sharp maximal functions

Fujii, Nobuhiko

doi:10.1090/S0002-9939-1989-0946637-8

A proof of the Fefferman-Stein-Strömberg inequality for the sharp maximal functions
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by Nobuhiko Fujii

Proc. Amer. Math. Soc. 106 (1989), 371-377

DOI: https://doi.org/10.1090/S0002-9939-1989-0946637-8

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Abstract:

We give another proof of a theorem of Strömberg for the Fefferman-Stein sharp maximal functions. Our method is based on a decomposition lemma which is due to the arguments of Carleson, Garnett and Jones for the functions of BMO, and it is valid for a two-weight setting under a condition which is equivalent to the ${A_\infty }$ condition in the case of equal weights.

References

A. P. Calderon and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. MR 52553, DOI 10.1007/BF02392130
Lennart Carleson, Two remarks on $H^{1}$ and BMO, Advances in Math. 22 (1976), no. 3, 269–277. MR 477058, DOI 10.1016/0001-8708(76)90095-5
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193. MR 447953, DOI 10.1007/BF02392215
John B. Garnett and Peter W. Jones, BMO from dyadic BMO, Pacific J. Math. 99 (1982), no. 2, 351–371. MR 658065, DOI 10.2140/pjm.1982.99.351
Jan-Olov Strömberg, Bounded mean oscillation with Orlicz norms and duality of Hardy spaces, Indiana Univ. Math. J. 28 (1979), no. 3, 511–544. MR 529683, DOI 10.1512/iumj.1979.28.28037