Bergman空间上Hankel算子的本性范数的刻划

Abstract

Abstract:

ＬｅｔΩｂｅａｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｖｅｘｄｏｍａｉｎｉｎ C^ｎ．Ｈａｎｋｅｌｏｐｅｒａｔｏｒ H_f（f∈L^２（Ω，ｄv）ｉｓｄｅｆｉｎｅｄｏｎＢｅｒｇｍａｎｓｐａｃｅA^２（Ω）,Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｏｂｔａｉｎｓｅｖｅｒａｌｅｑｕｖａｌｅｎｔｑｕａｎｔｉｔｉｅｓｏｆ‖H_f‖ｅｓｓ（ｔｈｅｅｓｓｅｎｔｉａｌｎｏｒｍｏｆH_f）．

Key words: Ｂｏｕｎｄｅｄｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｖｅｘｄｏｍａｉｎ, ＢｅｒｇｍａｎＳｐａｃｅ, Ｈａｎｋｅｌｏｐｅｒａｔｏｒ, Ｅｓｓｅｎｔｉａｌｎｏｒｍ．

CLC Number:

GAO Jin-Shou. The Chaaracterization of the Essential Norm of the Hankel Operators on Bergman Spaces[J].Acta mathematica scientia,Series A, 2000, 20(1): 41-47.

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１　ＲａｎｇｅＲＭ．ＨｏｌｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓａｎｄＩｎｔｅｇｒａｌＲｅｐｒｅｓｅｎｔａｔｉｏｎｓｉｎＳｅｖｅｒａｌｃｏｍｐｌｅｘＶａｒｉａｂｌｅｓ．ＮｅｗＹｏｒｋ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ，１９８６
２　ＢｅａｔｒｏｕｓＦ．L^PＥｓｔｉｍａｔｉｏｎｆｏｒｅｘｔｅｎｓｉｏｎｓｏｆｈｏｌｏｍｏｒｐｈｉｃｆｕｎｃｔｉｏｎｓ．ＭｉｃｈｉｇａｎＭａｔｈＪ，１９８５，３２：３６１－３８０
３　程民德，邓东皋，龙瑞麟．实分析．北京：高等教育出版社，１９９３
４　ＬｉＨｕｉｐｉｎｇ．ＨａｎｋｅｌｏｐｅｒａｔｏｒｓｏｎＢｅｒｇｍａｎｓｐａｃｅｓｏｆｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｖｅｘｄｏｍａｉｎｓ．ＩｎｔｅｒＥｑｕａｔｏｐｅｒＴｈ，１９９４，１９：４５８－４７６
５　ＢｅｒｎｄｔｓｓｏｎＢ，ＡｒｄｅｒｓｓｏｎＭ．ＨｅｎｋｉｎＲａｍｉｒｅｚｆｏｒｍｕｌａｓｗｉｔｈｗｅｉｇｈｔｆａｃｔｏｒｓ．ＡｎｎＩｎｓｔＦｏｕｒｉｅｒ，１９８２，１２：９１－１１０
６　ＺｈｕＫｅｈｅ．Ｏｐｅｒａｔｏｒｔｈｅｏｒｙｉｎｆｕｎｃｔｉｏｎｓｐａｃｅ．ＮｅｗＹｏｒｋ：ＭａｒｃｅｌＤｅｋｋｅｒ，１９９０
７　ＬｉＨｕｉｐｉｎｇ．ＳｃｈａｔｔｅｎｃｌａｓｓＨａｎｋｅｌｏｐｅｒａｔｏｒｓｏｎｔｈｅＢｅｒｇｍａｎｓｐａｃｅｏｆｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｖｅｘｄｏｍａｉｎｓ，ＰｒｏｃＡｍｅｒＭａｔｈＳｏｃ，１９９３，１１９（４）：１２１１－１２２１
８　ＬｕｅｋｉｎｇＤＨ．ＣｈｅｒａｃｔｅｒｉｚａｔｉｏｎｏｆＣｅｒｔａｉｎｃｌａｓｓｅｓｏｆＨａｎｋｅｌｏｐｅｒａｔｏｒｓｏｎＢｅｒｇｍａｎｓｐａｃｅｏｆｔｈｅＵｎｉｔｄｉｓｋ．ＪＦｕｎｃｔＡｎａｌ，１９９２，１１０：２４７－２７２
９　ＫｒａｎｔｚＳＧ．Ｆｕｎｃｔｉｏｎｔｈｅｏｒｙｏｆｓｅｖｅｒａｌｃｏｍｐｌｅｘｖａｒｉａｂｌｅｓ．ＮｅｗＹｏｒｋ：ＪｏｈＷｉｌｅｙａｎｄＳｏｎｓ，１９８２

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The Chaaracterization of the Essential Norm of the Hankel Operators on Bergman Spaces

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