A note on commutators of Bochner-Riesz operator

Shanzhen Lu , Xia Xia

Front. Math. China ›› 2007, Vol. 2 ›› Issue (3) : 439 -446.

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Front. Math. China ›› 2007, Vol. 2 ›› Issue (3) : 439 -446. DOI: 10.1007/s11464-007-0026-1
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A note on commutators of Bochner-Riesz operator

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Abstract

In terms of continuous decomposition and choosing an appropriate BMO function, the authors obtain a sharp necessary condition for Lp boundedness of the commutators generated by Bochner-Riesz operators below the critical index and BMO functions.

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Commutator / Bochner-Riesz operator / BMO function

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Shanzhen Lu, Xia Xia. A note on commutators of Bochner-Riesz operator. Front. Math. China, 2007, 2(3): 439-446 DOI:10.1007/s11464-007-0026-1

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References

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Herz C. On the mean inversion of Fourier and Hankel transforms. Proc Nat Acad Sci USA, 1954, 40: 996-999.

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Carleson L., Sjölin P. Oscillatory integrals and multiplier problem for disc. Studia Math, 1972, 44(3): 287-299.
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Hu G. E., Lu S. Z. The commutator of the Bochner-Riesz operator. Tôhoku Math J, 1996, 48: 259-266.
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