Positive Toeplitz Operators Between the Harmonic Bergman Spaces |
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| Authors: | Boo Rim Choe Hyungwoon Koo Heungsu Yi |
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| Institution: | (1) Department of Mathematics, Korea University, Seoul, 136-701, Korea;(2) Department of Mathematics, Research Institute of Basic Sciences, Kwangwoon University, Seoul, 139-701, Korea |
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| Abstract: | On the setting of the upper half space we study positive Toeplitz operators between the harmonic Bergman spaces. We give characterizations of bounded and compact positive Toeplitz operators taking a harmonic Bergman space b
p
into another b
q
for 1<p< , 1<q<. The case p=1 or q=1 seems more intriguing and is left open for further investigation. Also, we give criteria for positive Toeplitz operators acting on b
2 to be in the Schatten classes. Some applications are also included. |
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| Keywords: | Carleson measures positive Toeplitz operators multipliers harmonic Bergman functions half-space |
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