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Boundedness of Berezin transform on Herz spaces
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In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of Cn. And we provide the integral estimates concerning plurihar-monic kernel functions. Using this, we nally obtain the growth estimates of the Berezin transforms on such Herz spaces.
Abstract
In this paper, we give the condition for the boundedness of the Berezin transforms on Herz spaces with a normal weight on the unit ball of Cn. And we provide the integral estimates concerning plurihar-monic kernel functions. Using this, we nally obtain the growth estimates of the Berezin transforms on such Herz spaces.
참고문헌 (5)
- B. R. Choe, "Note on the Berezin transform on Herz spaces", RIMS Kyokuroku, 1519, pp.21~37 (2006)
- B. R. Choe, "Positive Toeplitz operators of Schatten-Herz type", Nagoya Math. J, 185, pp.31~62 (2007)
- M. Loaiza, M, "Herz classes and Toeplitz operators in the disk", Integral Equations Operator Theory, 53(2), pp.287~296 (2005)
- K. Na, "Positive Schatten(-Herz) class Toeplitz operators on pluriharmonic Bergman spaces", Integral Equations Operator Theory, 64(3), pp.409~428 (2009)
- W. Rudin, "Function Theory in the Unit Ball of Cn" (1980), Springer Verlag
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