Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C
2018 ◽
Vol 2018
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pp. 1-11
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Keyword(s):
We study the compactness of some classes of bounded operators on the Bergman space with variable exponent. We show that via extrapolation, some results on boundedness of the Toeplitz operators with general L1 symbols and compactness of bounded operators on the Bergman spaces with constant exponents can readily be extended to the variable exponent setting. In particular, if S is a finite sum of finite products of Toeplitz operators with symbols from class BT, then S is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disc.
2000 ◽
Vol 62
(2)
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pp. 273-285
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Keyword(s):
2002 ◽
Vol 54
(6)
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pp. 1165-1186
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Keyword(s):
2011 ◽
Vol 2011
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pp. 1-26
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2016 ◽
Vol 61
(8)
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pp. 1090-1106
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1995 ◽
Vol 37
(3)
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pp. 303-309
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Keyword(s):
2003 ◽
Vol 2003
(46)
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pp. 2929-2945
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Keyword(s):