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Results on weighted norm inequalities for multipliers. (English) Zbl 0427.42004

##### MSC:
 42B15 Multipliers for harmonic analysis in several variables 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
##### Keywords:
weight functions; norm inequalities
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##### References:
 [1] A. P. Calderón, Mary Weiss, and A. Zygmund, On the existence of singular integrals, Singular integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), Amer. Math. Soc., Providence, R.I., 1967, pp. 56 – 73. [2] A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no. 2, 101 – 171. · Zbl 0355.46021 · doi:10.1016/S0001-8708(77)80016-9 · doi.org [3] R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241 – 250. · Zbl 0291.44007 [4] A. Cordoba and C. Fefferman, A weighted norm inequality for singular integrals, Studia Math. 57 (1976), no. 1, 97 – 101. · Zbl 0356.44003 [5] C. Fefferman and E. M. Stein, \?^\? spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137 – 193. · Zbl 0257.46078 · doi:10.1007/BF02392215 · doi.org [6] I. I. Hirschman, The decomposition of Walsh and Fourier series, Mem. Amer. Math. Soc. No. 15 (1955), 65. · Zbl 0067.04102 [7] Lars Hörmander, Estimates for translation invariant operators in \?^\? spaces, Acta Math. 104 (1960), 93 – 140. · Zbl 0093.11402 · doi:10.1007/BF02547187 · doi.org [8] Richard Hunt, Benjamin Muckenhoupt, and Richard Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227 – 251. · Zbl 0262.44004 [9] P. Jones, (to appear). [10] Makoto Kaneko and Shigeki Yano, Weighted norm inequalities for singular integrals, J. Math. Soc. Japan 27 (1975), no. 4, 570 – 588. · Zbl 0309.44004 · doi:10.2969/jmsj/02740570 · doi.org [11] Paul Krée, Sur les multiplicateurs dans \cal\?\?^\? avec poids, Ann. Inst. Fourier (Grenoble) 16 (1966), 91 – 121. · Zbl 0145.38402 [12] D. Kurtz, Littlewood-Paley and multiplier theorems on weighted $${L^p}$$ spaces, Ph.D. Dissertation, Rutgers University, 1978. · Zbl 0436.42012 [13] Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207 – 226. · Zbl 0236.26016 [14] Benjamin Muckenhoupt and Richard L. Wheeden, Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Math. Soc. 161 (1971), 249 – 258. · Zbl 0226.44007 [15] Benjamin Muckenhoupt and Richard L. Wheeden, Norm inequalities for the Littlewood-Paley function \?*_\?, Trans. Amer. Math. Soc. 191 (1974), 95 – 111. · Zbl 0289.44005 [16] B. Muckenhoupt, R. Wheeden and W.-S. Young, (to appear). [17] Elias M. Stein, Interpolation of linear operators, Trans. Amer. Math. Soc. 83 (1956), 482 – 492. · Zbl 0072.32402 [18] Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. · Zbl 0207.13501 [19] E. M. Stein and G. Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc. 87 (1958), 159 – 172. · Zbl 0083.34301 [20] Hans Triebel, Spaces of distributions with weights. Multipliers in \?_\?-spaces with weights, Math. Nachr. 78 (1977), 339 – 355. · Zbl 0376.46020 · doi:10.1002/mana.19770780131 · doi.org
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