Littlewood-Paley operators on BMO
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- by Douglas S. Kurtz PDF
- Proc. Amer. Math. Soc. 99 (1987), 657-666 Request permission
Abstract:
Two Littlewood-Paley operators, the area integral and the function $g_\lambda ^ *$, are considered as operators on functions of bounded mean oscillation. It is proved that the image of a BMO function under one of these operators is either equal to infinity almost everywhere or is in BMO.References
- 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
- F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
- Douglas S. Kurtz, Rearrangement inequalities for Littlewood-Paley operators, Math. Nachr. 133 (1987), 71–90. MR 912421, DOI 10.1002/mana.19871330106
- José Luis Rubio de Francia, Francisco J. Ruiz, and José L. Torrea, Les opérateurs de Calderón-Zygmund vectoriels, C. R. Acad. Sci. Paris Sér. I Math. 297 (1983), no. 8, 477–480 (French, with English summary). MR 736248 X. Shi and A. Torchinsky (oral communication).
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Si Lei Wang, Some properties of the Littlewood-Paley $g$-function, Classical real analysis (Madison, Wis., 1982) Contemp. Math., vol. 42, Amer. Math. Soc., Providence, RI, 1985, pp. 191–202. MR 807991, DOI 10.1090/conm/042/807991
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 657-666
- MSC: Primary 42B25; Secondary 42B20
- DOI: https://doi.org/10.1090/S0002-9939-1987-0877035-1
- MathSciNet review: 877035