Toeplitz operators with L 1 symbols on Bergman spaces in the unit ball of

Compact Operators on the Bergman Spaces with Variable Exponents on the Unit Disc of C

“…We note here that this result was proved in [3] in the Bergman spaces , where is a constant. We also have the following result on compactness.…”

“…In this paper, we will extend the results in [3,7] on boundedness and compactness of operators for the Bergman spaces with constant exponents to the Bergman spaces with variable exponents.…”

“…This theorem is well known in the Bergman spaces with constant exponents; for example, see [3,7]. However, the techniques here are different from those used in either of the papers for both the proof of boundedness and compactness.…”

“…The behaviour of these operators on the Hardy spaces, Bergman spaces, and Fock spaces has been studied widely and a lot of results are available in the literature. The characterization of compactness has been studied in [2][3][4][5][6][7][8] just to cite a few. Given Ω ⊂ R , a measurable function : Ω → [1, ∞) will be called a variable exponent.…”

Compactness via the Berezin transform of radial operators on the generalized Fock spaces

“…This subject has generated a lot of research, see for example [1,2,7,8,13,17,18,20]. In [13] it is shown that (1.7) is equivalent to the compactness of a bounded operator on the weighted Bergman spaces ( , ) for > 1, > −1 and…”