拟微分算子在$H^p(\omega)$上的有界性

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CLC Number:

O174.2

Yongming Wen,Xianming Hou. The Boundedness of Pseudodifferential Operators on $H^p(\omega)$[J].Acta mathematica scientia,Series A, 2021, 41(2): 303-312.

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References 23

1	Alvarez J , Hounie J . Estimates for the kernel and continuity properties of pseudo-differential operators. Ark Mat, 1990, 28 (1/2): 1- 22
2	Atiyah M F , Singer I M . The index of elliptic operators I. Ann of Math, 1968, 87 (3): 484- 530 doi: 10.2307/1970715
3	Beltran D . Control of pseudo-differential operators by maximal functions via weighted inequalities. Trans Amer Math Soc, 2019, 371 (5): 3117- 3143
4	Beltran D , Cladek L . Sparse bounds for pseudo-differential operators. J Anal Math, 2020, 140 (1): 89- 116 doi: 10.1007/s11854-020-0083-x
5	Bownik M , Li B D , Yang D C , et al. Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ Math J, 2008, 57 (7): 3065- 3100 doi: 10.1512/iumj.2008.57.3414
6	Cao M M , Xue Q Y , Yabuta K . Weak and strong type estimates for the multilinear pseudo-differential operators. J Funct Anal, 2020, 278 (10): 46
7	Chanillo S , Torchinsky A . Sharp function and weighted $L.p$ estimates for a class of pseudo-differential operators. Ark Mat, 1986, 24 (1): 1- 25 doi: 10.1007/BF02384387
8	Coifman R R . A real variable characterization of $H^p$. Studia Math, 1974, 51, 269- 274 doi: 10.4064/sm-51-3-269-274
9	Coifman R R , Rochberg R , Weiss G . Factorization theorems for Hardy spaces in several variables. Ann of Math (2), 1976, 103 (3): 611- 635 doi: 10.2307/1970954
10	Coifman R R , Weiss G . Extensions of Hardy spaces and their use in analysis. Bull Amer Math Soc, 1977, 83 (4): 569- 645 doi: 10.1090/S0002-9904-1977-14325-5
11	Deng Y L , Long S C . Pseusodifferential operators on weighted Hardy spaces. J Funct Spaces, 2020, doi: 10.1155/2020/7154125
12	Fefferman C . $L^p$ bounds for pseudo-differential operators. Israel J Math, 1973, 14, 413- 417 doi: 10.1007/BF02764718
13	Fefferman C , Stein E M . $H^p$ spaces of several variables. Acta Math, 1972, 129, 137- 193 doi: 10.1007/BF02392215
14	García-Cuerva L . Weighted $H^p$ Spaces. Warszawa: Polish Scientific Publishers, 1979,
15	Hörmander L . Pseudo-differential operators and non-elliptic boundary problems. Ann of Math (2), 1966, 83, 129- 209 doi: 10.2307/1970473
16	Hörmander L . On the $L^2$ continuity of pseudo-differential operators. Comm Pure Appl Math, 1971, 24, 529- 535 doi: 10.1002/cpa.3160240406
17	Hounie J , Kapp R A d S . Pseudo-differential operators on local Hardy spaces. J Fourier Anal Appl, 2009, 15 (2): 153- 178 doi: 10.1007/s00041-008-9021-5
18	Kohn J J , Nirenberg L . An algebra of pseudo-differential operators. Comm Pure Appl Math, 1965, 18, 269- 305 doi: 10.1002/cpa.3160180121
19	Michalowski N , Rule D J , Staubach W . Weighted norm inequalities for pseudo-differential operators defined by amplitudes. J Funct Anal, 2010, 258 (12): 4183- 4209 doi: 10.1016/j.jfa.2010.03.013
20	Michalowski N , Rule D J , Staubach W . Weighted $L^p$ boundedness of pseudo-differential operators and applications. Canad Math Bull, 2012, 55 (3): 555- 570 doi: 10.4153/CMB-2011-122-7
21	Strömberg J , Torchinsky A . Weighted Hardy spaces. New York: Springer-Verlag, 1989
22	Xiao J W , Jiang Y S , Gao W H . Bilinear pseudo-differential operators on local Hardy spaces. Acta Math Sin (Engl Ser), 2012, 28 (2): 255- 266 doi: 10.1007/s10114-012-0283-0
23	Yabuta K . A note on weighted norm inequalities for pseudodifferential operators. Bull Fac Sci Ibaraki Univ Ser A, 1986, 18, 7- 12 doi: 10.5036/bfsiu1968.18.7

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The Boundedness of Pseudodifferential Operators on $H^p(\omega)$

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