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Positive Schatten class Toeplitz operators on the ball

Boo Rim Choe, Hyungwoon Koo, Young Joo Lee (2008)

Studia Mathematica

On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.

Positive Toeplitz operators between the pluriharmonic Bergman spaces

Eun Sun Choi (2008)

Czechoslovak Mathematical Journal

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 < in terms of certain Carleson and vanishing Carleson measures.

Potential spaces on fractals

Jiaxin Hu, Martina Zähle (2005)

Studia Mathematica

We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered.

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