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研究生:李明憶
研究生(外文):Ming-Yi Lee
論文名稱:奇異積分算子的加權模不等式
論文名稱(外文):Weighted Norm Inequalities of Singular Integral Operators
指導教授:林欽誠
指導教授(外文):chin-cheng Lin
學位類別:博士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:54
中文關鍵詞:加權哈弟空間分子刻劃
外文關鍵詞:weighted Hardy spacesmolecular characterization
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Cover
Contents
Chapter 1. Introduction
Chapter 2. Ap Weight
Chapter 3. Weighted Hardy spaces
Chapter 4. Hilbert transform and Riesztransform
Chapter 5. Bochner-Riesz means
Chapter 6. Riesz potential operators
Chapter 7. Marcinkiewicz integral
References


[B] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), 175-207.[BCP] A. Benedek, A. Calder´on and R. Panzone, Convolution operators on Banach space valued functions, Proc. Nat. Acad. Sci. USA 48 (1962), 356-365.[C] L. Colzani, Hardy and Lipschitz spaces on unit spheres, ph.D. Thesis, Washington University, St Louis, 1982.[Co] R. R. Coifman, A real-variable characterization of Hp, Studia Math. 51 (1974), 269-274.[CF] R. R. Coifman and C. Fe erman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250.[CTW] L. Colzani, M. Taibleson, and G. Weiss, Maximal estimates for Ces`aro and Riesz means on sphere, Indiana Univ. Math. J. 33 (1984), 873-889.[D] J. Duoandikoetxea, Weighted norm inequalities for homogeneous singular integrals, Trans. Amer. Math. Soc. 336 (1993), 869-880.[DFP1]Y. Ding, D. Fan, and Y. Pan, Weighted boundedness for a class of rough Marcinkiewicz integral, Indiana Univ. Math. J. 48 (1999), 1037-1055.[DFP2] _ Lp-boundedness of Marcinkiewicz integrals with Hardy space function kernels, Acta Math. Sinica (English series) 16 (2000), 593-600.[DL1] Y. Ding, and S. Lu, Weighted norm inequalities for fractional integral operators with rough kernel, Can. J. Math. 50(1) (1998), 29-39.[DL2] _ Homogeneous fractional integrals on Hardy spaces, Tohoku Math. J. 52 (2000), 153-162.[FS] C. Fefferman and E. M. Stein, Hp spaces of several variables, Acta Math. 129 (1972), 137-193.[G] J. Garc´ıa-Cuerva, Weighted Hp spaces, Dissertations Math. 162 (1979), 1-63.[GR] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North Holland, 1985.[GW] R. F. Gundy and R. L. Wheeden, Weighted integral inequalities for nontangential maximal function, Lusin area integral, and Walsh-Paley series, Studia Math. 49 (1974), 107-124.[HMW] R. Hunt, B. Muckenhoupt, and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251.[K] D. S. Kurtz, Littlewood-Paley and multiplies theorems on weighted Lp spaces, Trans. Amer. Math. Soc. 259 (1980), 235-254.[KW] D. S. Kurtz and R. L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc 255, 343-362.[L] R. H. Latter, A characterization of Hp(Rn) in terms of atoms, studia math. 62 (1978), 93-101.[LL] M.-Y. Lee and C.-C. Lin, The molecular characterization of weighted Hardy spaces, J. Funct. Anal. 188 (2002), 442-460.[M] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207-226.[R] V. S. Rychkov, Littlewood-Paley theory and function spaces with A^loc_p weights, Math. Nachr. 224 (2001), 145-180. [S1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970.[S2] _ On the function of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc. 88 (1958), 430-466.[S3] _ Harmonic Analysis, Princeton Univ. Press, Princeton, NJ, 1993.[Sa1] S. Sato, Weak type estimates for some maximal operators on the weighted Hardy spaces, Ark. Mat. 33 (1995), 377-384.[Sa2] _ Divergence of the Bochner-Riesz means in the weighted Hardy spaces, Studia Math. 118 (1996), 261-275.[Sj] P. Sj¨olin, Convolution with oscillating kernels in Hp spaces, J. London Math. Soc. 23 (1981), 442-454.[ST] J.-O. Str¨omberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Mathematics, vol. 1381, Springer-Verlag, 1989.[STW] E. M. Stein, M. H. Taibleson, and G. Weiss, Weak type estimates for maximal operators on certain Hp classes, Rend. Circ. Mat. Palermo. 2 (1981), suppl. 1, 81-97.[SW1] E. M. Stein and G.Weiss, Interpolation of operators with change of measures, Trans. Amer. Math. Soc 87 (1958), 159-172.[SW2] E. M. Stein and G. Weiss, On the theory of harmonic functions of several variables I: The theory of Hp spaces, Acta Math. 103 (1960), 25-62.[StW] J.-O. Str¨omberg and R. L. Wheeden, fractional integrals on weighted Hp and Lp spaces, Trans. Amer. Math. Soc 287 (1985), 293-321.[TW] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Ast´erisque 77 (1980), Soci´et´e Math. de France, Paris, 67-149.[TWa] A. Torchinsky and S. Wang, A note on the Marcinkiewicz integral, Coll. Math. 61-62 (1990), 235-243.

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