Toeplitz operators and Herz spaces on the half-space (Q2480703)

The paper is devoted to the study of Toeplitz operators on the harmonic Bergman space on the upper half-space in \(\mathbb{R}^n\) with symbols being positive Borel measures. The authors characterize their Schatten--Herz \(S_{p,q}\) class membership in terms of certain averaging functions and the Berezin transform. The following ranges of parameters are considered: \(1\leq p\leq\infty\), \(1\leq q\leq\infty\) or \(q=0\). Note that these results were further generalized to the case \(0<p,q\leq\infty\) by \textit{B.\,R.\thinspace Choe, H.\,Koo} and \textit{Y.\,J.\thinspace Lee} [Potential Anal.\ 27, No.\,1, 73--100 (2007; Zbl 1140.47013)].