Toeplitz operators on the weighted harmonic Bergman spaces
  In this paper, we study Toeplitz operators on the weighted harmonic Bergman spaces with nonnegative symbols, the weights we choose here are Muckenhoupt A_2 weights. Results obtained include characterizations of bounded Toeplitz operators, compact Toeplitz operators, invertible Toeplitz operators and Toeplitz operators in the Schatten classes. 
Zipeng Wang and Xianfeng Zhao
math.FA