Bergman projections, Berezin transforms and Cauchy transform on exponential Orlicz spaces and Lorentz-Zygmund spaces.

We establish the mapping properties of the Bergman projections, the harmonic Bergman projections, the Cesáro operator and the Hilbert matrix on exponential Orlicz spaces and Zygmund spaces. We also have the mapping properties of the Berezin transform on Zygmund spaces. A sharpened result for the mapping properties of the Cauchy transform from the Lebesgue spaces to space of bounded function is also obtained. [ABSTRACT FROM AUTHOR]