Geodesic
Positive Toeplitz operators between the pluriharmonic Bergman spaces
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 93-111.

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We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space $b^p$ into another $b^q$ for $1 p, q \infty $ in terms of certain Carleson and vanishing Carleson measures.
Classification : 31B05, 31C10, 46E15, 47B35
Keywords: Toeplitz operators; pluriharmonic Bergman spaces; Carleson measure 
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Choi, Eun Sun. Positive Toeplitz operators between the pluriharmonic Bergman spaces. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 1, pp. 93-111. http://geodesic.mathdoc.fr/item/CMJ_2008__58_1_a6/