Abstract. Motivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaiza et al.

We obtain optimal size estimates of the harmonic Bergman kernel and its derivatives on smooth domains. Based on these estimates we derive mapping properties of the harmonic Bergman projection on Lebesgue spaces and Lipschitz spaces. Academic Press

This study indicates that IL-1RA could be a candidate gene for susceptibility to schizophrenia.

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