Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (3): 241-246.
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Solvability and Hypoellipticity for Operate Lm&mu|on the Heisenberg Group Hn
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Abstract:
In this paper ,explicit fundament solution um for partial differential oprator Lmμ on the Heisenberg group Hn is given .By using this um,the solvability and teh hypoellipticity for operator Lmμ are studied.
Key words: Ｈｅｉｓｅｎｂｅｒｇｇｒｏｕｐ, Ｆｕｎｄａｍｅｎｔａｌｓｏｌｕｔｉｏｎ, Ｓｏｌｖａｂｉｌｉｔｙ, Ｈｙｐｏｅｌｌｉｐｔｉｃｉｔｙ
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Ma Yulan Luo Xuebo.
Solvability and Hypoellipticity for Operate Lm&mu|on the Heisenberg Group Hn[J].Acta mathematica scientia,Series A, 1999, 19(3): 241-246.
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URL: http://121.43.60.238/sxwlxbA/EN/
http://121.43.60.238/sxwlxbA/EN/Y1999/V19/I3/241
１ ＦｏｌｌａｎｄＧ Ｂ，ＳｔｅｉｎＥ Ｍ．Ｅｓｔｉｍａｔｅｓｆｏｒｔｈｅ∂b-ｃｏｍｐｌｅｘａｎｄａｎａｌｙｓｉｓｏｎｔｈｅ Ｈｅｉｓｅｎｂｅｒｇｇｒｏｕｐ．Ｃｏｍｍ Ｐｕｒｅ ＡｐｐｌＭａｔｈ，１９７４，２７：４２９－５２２ ２ ＦｏｌｌａｎｄＧＢ．ＳｕｂｅｌｌｉｐｔｉｃｅｓｔｉｍａｔｅｓａｎｄｆｕｎｃｔｉｏｎｓｐａｃｅｏｎｎｉｌｐｏｔｅｎｔＬｉｅｇｒｏｕｐ．Ａｒｋ Ｍａｔ，１９７５，１３：１６１－２０７ ３ ＦｏｌｌａｎｄＧＢ．ＨａｒｍｏｎｉｃＡｎａｌｙｓｉｓｉｎＰｈａｓｅＳｐａｃｅ．ＰｒｉｎｃｅｔｏｎＵｎｉｖＰｒｅｓｓ，１９８９ ４ Ｈ¨ｏｒｍａｎｄｅｒＬ．ＴｈｅａｎａｌｙｓｉｓｏｆｌｉｎｅａｒｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｏｐｅｒａｔｏｒｓＩ．Ｂｅｒｌｉｎ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８３，６８－６９ ５ ＡｎＹｏｕｓｈａｎ，ＬｕｏＸｕｅｂｏ．ＦｕｎｄａｍｅｎｔａｌｓｏｌｕｔｉｏｎｓｆｏｒｏｐｅｒａｔｏｒLUMｏｎｔｈｅ Ｈｅｉｓｅｎｂｅｒｇｇｒｏｕp Hn．ＣｈｉｎｅｓｅＳｃｉＢｕｌｌ， １９８９，１２：８８５－８８８ ６ ＮｅｔｏＪＢ．ＡｎＩｎｔｒｏｄｕｃｔｉｏｎｔｏｔｈｅＴｈｅｏｒｙｏｆＤｉｓｔｒｉｂｕｔｉｏｎｓ．Ｎｅｗ Ｙｏｒｋ：ＭａｒｃｅｌＤｅｋｋｅｒＩｎｃ．１９７３ ７ ＪｉａｎｇＹａｐｉｎｇ，ＬｕｏＸｕｅｂｏ．ＥｘｐｌｉｃｉｔｆｕｎｄａｍｅｎｔａｌｓｏｌｕｔｉｏｎｓｆｏｒａｃｌａｓｓｏｆｌｅｆｔｉｎｖａｒｉａｎｔｏｐｅｒａｔｏｒｓｏｎＬｉｅｇｒｏｕｐ G d1+d2 .ＡｃｔａＭａｔｈ，１９９３，９（２）：１８４－１９４ ８ ＢｅａｌｓＲ，ＧｒｅｉｎｅｒＲ．ＣａｌｃｕｌｕｓｏｎＨｅｉｓｅｎｂｅｒｇ Ｍａｎｉｆｏｌｄｓ．ＰｒｉｎｃｅｔｏｎＵｎｉｖＰｒｅｓｓ，１９８８ ９ ＧａｖｅａｕＢ．Ｐｒｉｎｃｉｐｌｅｄｅｍｏｉｎｄｒｅａｃｔｉｏｎｐｒｏｐａｇａｔｉｏｎｄｅｌａｃｈａｌｅｕｒｅｔｅｓｔｉｍｅｅｓｓｏｕｓｅｌｌｉｐｔｉｑｕｅｓｓｕｒｃｅｒｔａｉｎｇｒｏｕｐｓｎｉｌｐoｔｅｎｔｓ．ＡｃｔａＭａｔｈ，１９７７，１３９：９５－１５３ １０ ＴａｙｌｏｒＭ Ｅ．Ｎｏｎｃｏｍｍｕｔａｔｉｖｅｈａｒｍｏｎｉｃａｎａｌｙｓｉｓ．ＡｍｅｒＳｏｃｉＭｏｎｏｇｒａｐｈｓ，１９８６，２２
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